diff --git a/externs/olx.js b/externs/olx.js
index 1cdbffb777..61e8fed4e5 100644
--- a/externs/olx.js
+++ b/externs/olx.js
@@ -7376,7 +7376,7 @@ olx.view.FitOptions.prototype.maxZoom;
 /**
  * @typedef {{animate: boolean,
  *     attributions: Object.<string, ol.Attribution>,
- *     coordinateToPixelMatrix: ol.vec.Mat4.Number,
+ *     coordinateToPixelTransform: ol.Transform,
  *     extent: (null|ol.Extent),
  *     focus: ol.Coordinate,
  *     index: number,
@@ -7384,7 +7384,7 @@ olx.view.FitOptions.prototype.maxZoom;
  *     layerStatesArray: Array.<ol.LayerState>,
  *     logos: Object.<string, (string|Element)>,
  *     pixelRatio: number,
- *     pixelToCoordinateMatrix: ol.vec.Mat4.Number,
+ *     pixelToCoordinateTransform: ol.Transform,
  *     postRenderFunctions: Array.<ol.PostRenderFunction>,
  *     size: ol.Size,
  *     skippedFeatureUids: Object.<string, boolean>,
diff --git a/src/ol/dom/dom.js b/src/ol/dom/dom.js
index 9baa23a46b..78e7820dff 100644
--- a/src/ol/dom/dom.js
+++ b/src/ol/dom/dom.js
@@ -2,8 +2,15 @@ goog.provide('ol.dom');
 
 goog.require('goog.asserts');
 goog.require('goog.userAgent');
-goog.require('goog.vec.Mat4');
 goog.require('ol');
+goog.require('ol.vec.Mat4');
+
+
+/**
+ * @type {Array.<number>}
+ * @private
+ */
+ol.dom.tmpMat4_ = ol.vec.Mat4.create();
 
 
 /**
@@ -127,7 +134,7 @@ ol.dom.setTransform = function(element, value) {
 
 /**
  * @param {!Element} element Element.
- * @param {goog.vec.Mat4.Number} transform Matrix.
+ * @param {ol.Transform} transform Matrix.
  * @param {number=} opt_precision Precision.
  */
 ol.dom.transformElement2D = function(element, transform, opt_precision) {
@@ -136,45 +143,35 @@ ol.dom.transformElement2D = function(element, transform, opt_precision) {
   var i;
   if (ol.dom.canUseCssTransform3D()) {
     var value3D;
-
+    var transform3D = ol.vec.Mat4.fromTransform(ol.dom.tmpMat4_, transform);
     if (opt_precision !== undefined) {
       /** @type {Array.<string>} */
       var strings3D = new Array(16);
       for (i = 0; i < 16; ++i) {
-        strings3D[i] = transform[i].toFixed(opt_precision);
+        strings3D[i] = transform3D[i].toFixed(opt_precision);
       }
       value3D = strings3D.join(',');
     } else {
-      value3D = transform.join(',');
+      value3D = transform3D.join(',');
     }
     ol.dom.setTransform(element, 'matrix3d(' + value3D + ')');
   } else if (ol.dom.canUseCssTransform()) {
-    /** @type {Array.<number>} */
-    var transform2D = [
-      goog.vec.Mat4.getElement(transform, 0, 0),
-      goog.vec.Mat4.getElement(transform, 1, 0),
-      goog.vec.Mat4.getElement(transform, 0, 1),
-      goog.vec.Mat4.getElement(transform, 1, 1),
-      goog.vec.Mat4.getElement(transform, 0, 3),
-      goog.vec.Mat4.getElement(transform, 1, 3)
-    ];
+    /** @type {string} */
     var value2D;
     if (opt_precision !== undefined) {
       /** @type {Array.<string>} */
       var strings2D = new Array(6);
       for (i = 0; i < 6; ++i) {
-        strings2D[i] = transform2D[i].toFixed(opt_precision);
+        strings2D[i] = transform[i].toFixed(opt_precision);
       }
       value2D = strings2D.join(',');
     } else {
-      value2D = transform2D.join(',');
+      value2D = transform.join(',');
     }
     ol.dom.setTransform(element, 'matrix(' + value2D + ')');
   } else {
-    element.style.left =
-        Math.round(goog.vec.Mat4.getElement(transform, 0, 3)) + 'px';
-    element.style.top =
-        Math.round(goog.vec.Mat4.getElement(transform, 1, 3)) + 'px';
+    element.style.left = Math.round(transform[4]) + 'px';
+    element.style.top = Math.round(transform[5]) + 'px';
 
     // TODO: Add scaling here. This isn't quite as simple as multiplying
     // width/height, because that only changes the container size, not the
diff --git a/src/ol/geom/flat/transformflatgeom.js b/src/ol/geom/flat/transformflatgeom.js
index 29ca54a240..ae097afe57 100644
--- a/src/ol/geom/flat/transformflatgeom.js
+++ b/src/ol/geom/flat/transformflatgeom.js
@@ -1,32 +1,24 @@
 goog.provide('ol.geom.flat.transform');
 
-goog.require('goog.vec.Mat4');
-
 
 /**
  * @param {Array.<number>} flatCoordinates Flat coordinates.
  * @param {number} offset Offset.
  * @param {number} end End.
  * @param {number} stride Stride.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @param {Array.<number>=} opt_dest Destination.
  * @return {Array.<number>} Transformed coordinates.
  */
 ol.geom.flat.transform.transform2D = function(flatCoordinates, offset, end, stride, transform, opt_dest) {
-  var m00 = goog.vec.Mat4.getElement(transform, 0, 0);
-  var m10 = goog.vec.Mat4.getElement(transform, 1, 0);
-  var m01 = goog.vec.Mat4.getElement(transform, 0, 1);
-  var m11 = goog.vec.Mat4.getElement(transform, 1, 1);
-  var m03 = goog.vec.Mat4.getElement(transform, 0, 3);
-  var m13 = goog.vec.Mat4.getElement(transform, 1, 3);
   var dest = opt_dest ? opt_dest : [];
   var i = 0;
   var j;
   for (j = offset; j < end; j += stride) {
     var x = flatCoordinates[j];
     var y = flatCoordinates[j + 1];
-    dest[i++] = m00 * x + m01 * y + m03;
-    dest[i++] = m10 * x + m11 * y + m13;
+    dest[i++] = transform[0] * x + transform[2] * y + transform[4];
+    dest[i++] = transform[1] * x + transform[3] * y + transform[5];
   }
   if (opt_dest && dest.length != i) {
     dest.length = i;
diff --git a/src/ol/geom/simplegeometry.js b/src/ol/geom/simplegeometry.js
index ba60eea240..ca634a9dc5 100644
--- a/src/ol/geom/simplegeometry.js
+++ b/src/ol/geom/simplegeometry.js
@@ -294,7 +294,7 @@ ol.geom.SimpleGeometry.prototype.translate = function(deltaX, deltaY) {
 
 /**
  * @param {ol.geom.SimpleGeometry} simpleGeometry Simple geometry.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @param {Array.<number>=} opt_dest Destination.
  * @return {Array.<number>} Transformed flat coordinates.
  */
diff --git a/src/ol/map.js b/src/ol/map.js
index e07bd59e80..4e331d7bc4 100644
--- a/src/ol/map.js
+++ b/src/ol/map.js
@@ -7,7 +7,6 @@ goog.provide('ol.MapProperty');
 
 goog.require('goog.asserts');
 goog.require('goog.async.nextTick');
-goog.require('goog.vec.Mat4');
 goog.require('ol.Collection');
 goog.require('ol.CollectionEventType');
 goog.require('ol.MapBrowserEvent');
@@ -34,6 +33,7 @@ goog.require('ol.has');
 goog.require('ol.interaction');
 goog.require('ol.layer.Base');
 goog.require('ol.layer.Group');
+goog.require('ol.transform');
 goog.require('ol.object');
 goog.require('ol.proj');
 goog.require('ol.proj.common');
@@ -43,7 +43,6 @@ goog.require('ol.renderer.dom.Map');
 goog.require('ol.renderer.webgl.Map');
 goog.require('ol.size');
 goog.require('ol.structs.PriorityQueue');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -203,15 +202,15 @@ ol.Map = function(options) {
 
   /**
    * @private
-   * @type {goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.coordinateToPixelMatrix_ = goog.vec.Mat4.createNumber();
+  this.coordinateToPixelTransform_ = ol.transform.create();
 
   /**
    * @private
-   * @type {goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.pixelToCoordinateMatrix_ = goog.vec.Mat4.createNumber();
+  this.pixelToCoordinateTransform_ = ol.transform.create();
 
   /**
    * @private
@@ -764,8 +763,7 @@ ol.Map.prototype.getCoordinateFromPixel = function(pixel) {
   if (!frameState) {
     return null;
   } else {
-    var vec2 = pixel.slice();
-    return ol.vec.Mat4.multVec2(frameState.pixelToCoordinateMatrix, vec2, vec2);
+    return ol.transform.apply(frameState.pixelToCoordinateTransform, pixel.slice());
   }
 };
 
@@ -853,8 +851,8 @@ ol.Map.prototype.getPixelFromCoordinate = function(coordinate) {
   if (!frameState) {
     return null;
   } else {
-    var vec2 = coordinate.slice(0, 2);
-    return ol.vec.Mat4.multVec2(frameState.coordinateToPixelMatrix, vec2, vec2);
+    return ol.transform.apply(frameState.coordinateToPixelTransform,
+        coordinate.slice(0, 2));
   }
 };
 
@@ -1298,7 +1296,7 @@ ol.Map.prototype.renderFrame_ = function(time) {
     frameState = /** @type {olx.FrameState} */ ({
       animate: false,
       attributions: {},
-      coordinateToPixelMatrix: this.coordinateToPixelMatrix_,
+      coordinateToPixelTransform: this.coordinateToPixelTransform_,
       extent: extent,
       focus: !this.focus_ ? viewState.center : this.focus_,
       index: this.frameIndex_++,
@@ -1306,7 +1304,7 @@ ol.Map.prototype.renderFrame_ = function(time) {
       layerStatesArray: layerStatesArray,
       logos: ol.object.assign({}, this.logos_),
       pixelRatio: this.pixelRatio_,
-      pixelToCoordinateMatrix: this.pixelToCoordinateMatrix_,
+      pixelToCoordinateTransform: this.pixelToCoordinateTransform_,
       postRenderFunctions: [],
       size: size,
       skippedFeatureUids: this.skippedFeatureUids_,
diff --git a/src/ol/render.js b/src/ol/render.js
index b55141bd14..d8c66a7b2d 100644
--- a/src/ol/render.js
+++ b/src/ol/render.js
@@ -1,8 +1,7 @@
 goog.provide('ol.render');
 
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.render.canvas.Immediate');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -37,8 +36,7 @@ ol.render.toContext = function(context, opt_options) {
     canvas.style.height = size[1] + 'px';
   }
   var extent = [0, 0, canvas.width, canvas.height];
-  var transform = ol.vec.Mat4.makeTransform2D(goog.vec.Mat4.createNumber(),
-      0, 0, pixelRatio, pixelRatio, 0, 0, 0);
+  var transform = ol.transform.scale(ol.transform.create(), pixelRatio, pixelRatio);
   return new ol.render.canvas.Immediate(context, pixelRatio, extent, transform,
       0);
 };
diff --git a/src/ol/render/canvas/canvasimmediate.js b/src/ol/render/canvas/canvasimmediate.js
index b4af6db0db..3af236700e 100644
--- a/src/ol/render/canvas/canvasimmediate.js
+++ b/src/ol/render/canvas/canvasimmediate.js
@@ -5,7 +5,7 @@
 goog.provide('ol.render.canvas.Immediate');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.array');
 goog.require('ol.color');
 goog.require('ol.colorlike');
@@ -15,7 +15,6 @@ goog.require('ol.geom.flat.transform');
 goog.require('ol.has');
 goog.require('ol.render.VectorContext');
 goog.require('ol.render.canvas');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -32,7 +31,7 @@ goog.require('ol.vec.Mat4');
  * @param {CanvasRenderingContext2D} context Context.
  * @param {number} pixelRatio Pixel ratio.
  * @param {ol.Extent} extent Extent.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @param {number} viewRotation View rotation.
  * @struct
  */
@@ -59,7 +58,7 @@ ol.render.canvas.Immediate = function(context, pixelRatio, extent, transform, vi
 
   /**
    * @private
-   * @type {goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
   this.transform_ = transform;
 
@@ -227,9 +226,9 @@ ol.render.canvas.Immediate = function(context, pixelRatio, extent, transform, vi
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.tmpLocalTransform_ = goog.vec.Mat4.createNumber();
+  this.tmpLocalTransform_ = ol.transform.create();
 
 };
 ol.inherits(ol.render.canvas.Immediate, ol.render.VectorContext);
@@ -273,16 +272,12 @@ ol.render.canvas.Immediate.prototype.drawImages_ = function(flatCoordinates, off
     if (rotation !== 0 || this.imageScale_ != 1) {
       var centerX = x + this.imageAnchorX_;
       var centerY = y + this.imageAnchorY_;
-      ol.vec.Mat4.makeTransform2D(localTransform,
-          centerX, centerY, this.imageScale_, this.imageScale_,
-          rotation, -centerX, -centerY);
-      context.setTransform(
-          goog.vec.Mat4.getElement(localTransform, 0, 0),
-          goog.vec.Mat4.getElement(localTransform, 1, 0),
-          goog.vec.Mat4.getElement(localTransform, 0, 1),
-          goog.vec.Mat4.getElement(localTransform, 1, 1),
-          goog.vec.Mat4.getElement(localTransform, 0, 3),
-          goog.vec.Mat4.getElement(localTransform, 1, 3));
+      ol.transform.compose(localTransform,
+          centerX, centerY,
+          this.imageScale_, this.imageScale_,
+          rotation,
+          -centerX, -centerY);
+      context.setTransform.apply(context, localTransform);
     }
     context.drawImage(this.image_, this.imageOriginX_, this.imageOriginY_,
         this.imageWidth_, this.imageHeight_, x, y,
@@ -326,15 +321,12 @@ ol.render.canvas.Immediate.prototype.drawText_ = function(flatCoordinates, offse
     var x = pixelCoordinates[offset] + this.textOffsetX_;
     var y = pixelCoordinates[offset + 1] + this.textOffsetY_;
     if (this.textRotation_ !== 0 || this.textScale_ != 1) {
-      var localTransform = ol.vec.Mat4.makeTransform2D(this.tmpLocalTransform_,
-          x, y, this.textScale_, this.textScale_, this.textRotation_, -x, -y);
-      context.setTransform(
-          goog.vec.Mat4.getElement(localTransform, 0, 0),
-          goog.vec.Mat4.getElement(localTransform, 1, 0),
-          goog.vec.Mat4.getElement(localTransform, 0, 1),
-          goog.vec.Mat4.getElement(localTransform, 1, 1),
-          goog.vec.Mat4.getElement(localTransform, 0, 3),
-          goog.vec.Mat4.getElement(localTransform, 1, 3));
+      var localTransform = ol.transform.compose(this.tmpLocalTransform_,
+          x, y,
+          this.textScale_, this.textScale_,
+          this.textRotation_,
+          -x, -y);
+      context.setTransform.apply(context, localTransform);
     }
     if (this.textStrokeState_) {
       context.strokeText(this.text_, x, y);
diff --git a/src/ol/render/canvas/canvasreplay.js b/src/ol/render/canvas/canvasreplay.js
index 3370db2737..441188e481 100644
--- a/src/ol/render/canvas/canvasreplay.js
+++ b/src/ol/render/canvas/canvasreplay.js
@@ -9,7 +9,7 @@ goog.provide('ol.render.canvas.ReplayGroup');
 goog.provide('ol.render.canvas.TextReplay');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol');
 goog.require('ol.array');
 goog.require('ol.color');
@@ -24,7 +24,6 @@ goog.require('ol.object');
 goog.require('ol.render.IReplayGroup');
 goog.require('ol.render.VectorContext');
 goog.require('ol.render.canvas');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -117,9 +116,9 @@ ol.render.canvas.Replay = function(tolerance, maxExtent, resolution) {
 
   /**
    * @private
-   * @type {goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.renderedTransform_ = goog.vec.Mat4.createNumber();
+  this.renderedTransform_ = ol.transform.create();
 
   /**
    * @protected
@@ -135,15 +134,15 @@ ol.render.canvas.Replay = function(tolerance, maxExtent, resolution) {
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.tmpLocalTransform_ = goog.vec.Mat4.createNumber();
+  this.tmpLocalTransform_ = ol.transform.create();
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.tmpLocalTransformInv_ = goog.vec.Mat4.createNumber();
+  this.tmpLocalTransformInv_ = ol.transform.create();
 };
 ol.inherits(ol.render.canvas.Replay, ol.render.VectorContext);
 
@@ -223,7 +222,7 @@ ol.render.canvas.Replay.prototype.beginGeometry = function(geometry, feature) {
  * @private
  * @param {CanvasRenderingContext2D} context Context.
  * @param {number} pixelRatio Pixel ratio.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @param {number} viewRotation View rotation.
  * @param {Object.<string, boolean>} skippedFeaturesHash Ids of features
  *     to skip.
@@ -240,13 +239,13 @@ ol.render.canvas.Replay.prototype.replay_ = function(
     instructions, featureCallback, opt_hitExtent) {
   /** @type {Array.<number>} */
   var pixelCoordinates;
-  if (ol.vec.Mat4.equals2D(transform, this.renderedTransform_)) {
+  if (ol.array.equals(transform, this.renderedTransform_)) {
     pixelCoordinates = this.pixelCoordinates_;
   } else {
     pixelCoordinates = ol.geom.flat.transform.transform2D(
         this.coordinates, 0, this.coordinates.length, 2,
         transform, this.pixelCoordinates_);
-    goog.vec.Mat4.setFromArray(this.renderedTransform_, transform);
+    ol.transform.setFromArray(this.renderedTransform_, transform);
     goog.asserts.assert(pixelCoordinates === this.pixelCoordinates_,
         'pixelCoordinates should be the same as this.pixelCoordinates_');
   }
@@ -332,16 +331,9 @@ ol.render.canvas.Replay.prototype.replay_ = function(
           if (scale != 1 || rotation !== 0) {
             var centerX = x + anchorX;
             var centerY = y + anchorY;
-            ol.vec.Mat4.makeTransform2D(
-                localTransform, centerX, centerY, scale, scale,
-                rotation, -centerX, -centerY);
-            context.transform(
-                goog.vec.Mat4.getElement(localTransform, 0, 0),
-                goog.vec.Mat4.getElement(localTransform, 1, 0),
-                goog.vec.Mat4.getElement(localTransform, 0, 1),
-                goog.vec.Mat4.getElement(localTransform, 1, 1),
-                goog.vec.Mat4.getElement(localTransform, 0, 3),
-                goog.vec.Mat4.getElement(localTransform, 1, 3));
+            ol.transform.compose(localTransform,
+                centerX, centerY, scale, scale, rotation, -centerX, -centerY);
+            context.transform.apply(context, localTransform);
           }
           var alpha = context.globalAlpha;
           if (opacity != 1) {
@@ -358,14 +350,8 @@ ol.render.canvas.Replay.prototype.replay_ = function(
             context.globalAlpha = alpha;
           }
           if (scale != 1 || rotation !== 0) {
-            goog.vec.Mat4.invert(localTransform, localTransformInv);
-            context.transform(
-                goog.vec.Mat4.getElement(localTransformInv, 0, 0),
-                goog.vec.Mat4.getElement(localTransformInv, 1, 0),
-                goog.vec.Mat4.getElement(localTransformInv, 0, 1),
-                goog.vec.Mat4.getElement(localTransformInv, 1, 1),
-                goog.vec.Mat4.getElement(localTransformInv, 0, 3),
-                goog.vec.Mat4.getElement(localTransformInv, 1, 3));
+            ol.transform.invert(ol.transform.setFromArray(localTransformInv, localTransform));
+            context.transform.apply(context, localTransformInv);
           }
         }
         ++i;
@@ -402,15 +388,8 @@ ol.render.canvas.Replay.prototype.replay_ = function(
           x = pixelCoordinates[d] + offsetX;
           y = pixelCoordinates[d + 1] + offsetY;
           if (scale != 1 || rotation !== 0) {
-            ol.vec.Mat4.makeTransform2D(
-                localTransform, x, y, scale, scale, rotation, -x, -y);
-            context.transform(
-                goog.vec.Mat4.getElement(localTransform, 0, 0),
-                goog.vec.Mat4.getElement(localTransform, 1, 0),
-                goog.vec.Mat4.getElement(localTransform, 0, 1),
-                goog.vec.Mat4.getElement(localTransform, 1, 1),
-                goog.vec.Mat4.getElement(localTransform, 0, 3),
-                goog.vec.Mat4.getElement(localTransform, 1, 3));
+            ol.transform.compose(localTransform, x, y, scale, scale, rotation, -x, -y);
+            context.transform.apply(context, localTransform);
           }
 
           // Support multiple lines separated by \n
@@ -441,14 +420,8 @@ ol.render.canvas.Replay.prototype.replay_ = function(
           }
 
           if (scale != 1 || rotation !== 0) {
-            goog.vec.Mat4.invert(localTransform, localTransformInv);
-            context.transform(
-                goog.vec.Mat4.getElement(localTransformInv, 0, 0),
-                goog.vec.Mat4.getElement(localTransformInv, 1, 0),
-                goog.vec.Mat4.getElement(localTransformInv, 0, 1),
-                goog.vec.Mat4.getElement(localTransformInv, 1, 1),
-                goog.vec.Mat4.getElement(localTransformInv, 0, 3),
-                goog.vec.Mat4.getElement(localTransformInv, 1, 3));
+            ol.transform.invert(ol.transform.setFromArray(localTransformInv, localTransform));
+            context.transform.apply(context, localTransformInv);
           }
         }
         ++i;
@@ -565,7 +538,7 @@ ol.render.canvas.Replay.prototype.replay_ = function(
 /**
  * @param {CanvasRenderingContext2D} context Context.
  * @param {number} pixelRatio Pixel ratio.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @param {number} viewRotation View rotation.
  * @param {Object.<string, boolean>} skippedFeaturesHash Ids of features
  *     to skip.
@@ -580,7 +553,7 @@ ol.render.canvas.Replay.prototype.replay = function(
 
 /**
  * @param {CanvasRenderingContext2D} context Context.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @param {number} viewRotation View rotation.
  * @param {Object.<string, boolean>} skippedFeaturesHash Ids of features
  *     to skip.
@@ -1883,9 +1856,9 @@ ol.render.canvas.ReplayGroup = function(
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.hitDetectionTransform_ = goog.vec.Mat4.createNumber();
+  this.hitDetectionTransform_ = ol.transform.create();
 
 };
 
@@ -1919,9 +1892,10 @@ ol.render.canvas.ReplayGroup.prototype.finish = function() {
 ol.render.canvas.ReplayGroup.prototype.forEachFeatureAtCoordinate = function(
     coordinate, resolution, rotation, skippedFeaturesHash, callback) {
 
-  var transform = this.hitDetectionTransform_;
-  ol.vec.Mat4.makeTransform2D(transform, 0.5, 0.5,
-      1 / resolution, -1 / resolution, -rotation,
+  var transform = ol.transform.compose(this.hitDetectionTransform_,
+      0.5, 0.5,
+      1 / resolution, -1 / resolution,
+      -rotation,
       -coordinate[0], -coordinate[1]);
 
   var context = this.hitDetectionContext_;
@@ -1991,7 +1965,7 @@ ol.render.canvas.ReplayGroup.prototype.isEmpty = function() {
 /**
  * @param {CanvasRenderingContext2D} context Context.
  * @param {number} pixelRatio Pixel ratio.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @param {number} viewRotation View rotation.
  * @param {Object.<string, boolean>} skippedFeaturesHash Ids of features
  *     to skip.
@@ -2044,7 +2018,7 @@ ol.render.canvas.ReplayGroup.prototype.replay = function(context, pixelRatio,
 /**
  * @private
  * @param {CanvasRenderingContext2D} context Context.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @param {number} viewRotation View rotation.
  * @param {Object.<string, boolean>} skippedFeaturesHash Ids of features
  *     to skip.
diff --git a/src/ol/render/webgl/webglreplay.js b/src/ol/render/webgl/webglreplay.js
index 687c70b2ad..d615165e19 100644
--- a/src/ol/render/webgl/webglreplay.js
+++ b/src/ol/render/webgl/webglreplay.js
@@ -2,7 +2,7 @@ goog.provide('ol.render.webgl.ImageReplay');
 goog.provide('ol.render.webgl.ReplayGroup');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.extent');
 goog.require('ol.object');
 goog.require('ol.render.IReplayGroup');
@@ -116,16 +116,16 @@ ol.render.webgl.ImageReplay = function(tolerance, maxExtent) {
   this.opacity_ = undefined;
 
   /**
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    * @private
    */
-  this.offsetRotateMatrix_ = goog.vec.Mat4.createNumberIdentity();
+  this.offsetRotateMatrix_ = ol.transform.create();
 
   /**
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    * @private
    */
-  this.offsetScaleMatrix_ = goog.vec.Mat4.createNumberIdentity();
+  this.offsetScaleMatrix_ = ol.transform.create();
 
   /**
    * @type {number|undefined}
@@ -140,10 +140,16 @@ ol.render.webgl.ImageReplay = function(tolerance, maxExtent) {
   this.originY_ = undefined;
 
   /**
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    * @private
    */
-  this.projectionMatrix_ = goog.vec.Mat4.createNumberIdentity();
+  this.projectionMatrix_ = ol.transform.create();
+
+  /**
+   * @type {Array.<number>}
+   * @private
+   */
+  this.tmpMat4_ = ol.vec.Mat4.create();
 
   /**
    * @private
@@ -552,27 +558,25 @@ ol.render.webgl.ImageReplay.prototype.replay = function(context,
       false, 32, 28);
 
   // set the "uniform" values
-  var projectionMatrix = this.projectionMatrix_;
-  ol.vec.Mat4.makeTransform2D(projectionMatrix,
-      0.0, 0.0,
-      2 / (resolution * size[0]),
-      2 / (resolution * size[1]),
-      -rotation,
-      -(center[0] - this.origin_[0]), -(center[1] - this.origin_[1]));
+  var projectionMatrix = ol.transform.reset(this.projectionMatrix_);
+  ol.transform.scale(projectionMatrix, 2 / (resolution * size[0]), 2 / (resolution * size[1]));
+  ol.transform.rotate(projectionMatrix, -rotation);
+  ol.transform.translate(projectionMatrix, -(center[0] - this.origin_[0]), -(center[1] - this.origin_[1]));
 
-  var offsetScaleMatrix = this.offsetScaleMatrix_;
-  goog.vec.Mat4.makeScale(offsetScaleMatrix, 2 / size[0], 2 / size[1], 1);
+  var offsetScaleMatrix = ol.transform.reset(this.offsetScaleMatrix_);
+  ol.transform.scale(offsetScaleMatrix, 2 / size[0], 2 / size[1]);
 
-  var offsetRotateMatrix = this.offsetRotateMatrix_;
-  goog.vec.Mat4.makeIdentity(offsetRotateMatrix);
+  var offsetRotateMatrix = ol.transform.reset(this.offsetRotateMatrix_);
   if (rotation !== 0) {
-    goog.vec.Mat4.rotateZ(offsetRotateMatrix, -rotation);
+    ol.transform.rotate(offsetRotateMatrix, -rotation);
   }
 
-  gl.uniformMatrix4fv(locations.u_projectionMatrix, false, projectionMatrix);
-  gl.uniformMatrix4fv(locations.u_offsetScaleMatrix, false, offsetScaleMatrix);
+  gl.uniformMatrix4fv(locations.u_projectionMatrix, false,
+      ol.vec.Mat4.fromTransform(this.tmpMat4_, projectionMatrix));
+  gl.uniformMatrix4fv(locations.u_offsetScaleMatrix, false,
+      ol.vec.Mat4.fromTransform(this.tmpMat4_, offsetScaleMatrix));
   gl.uniformMatrix4fv(locations.u_offsetRotateMatrix, false,
-      offsetRotateMatrix);
+      ol.vec.Mat4.fromTransform(this.tmpMat4_, offsetRotateMatrix));
   gl.uniform1f(locations.u_opacity, opacity);
 
   // draw!
diff --git a/src/ol/renderer/canvas/canvasimagelayerrenderer.js b/src/ol/renderer/canvas/canvasimagelayerrenderer.js
index b70d79d333..0dd67c827d 100644
--- a/src/ol/renderer/canvas/canvasimagelayerrenderer.js
+++ b/src/ol/renderer/canvas/canvasimagelayerrenderer.js
@@ -1,7 +1,7 @@
 goog.provide('ol.renderer.canvas.ImageLayer');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.functions');
 goog.require('ol.ImageBase');
 goog.require('ol.ViewHint');
@@ -11,7 +11,6 @@ goog.require('ol.layer.Image');
 goog.require('ol.proj');
 goog.require('ol.renderer.canvas.Layer');
 goog.require('ol.source.ImageVector');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -31,13 +30,13 @@ ol.renderer.canvas.ImageLayer = function(imageLayer) {
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.imageTransform_ = goog.vec.Mat4.createNumber();
+  this.imageTransform_ = ol.transform.create();
 
   /**
    * @private
-   * @type {?goog.vec.Mat4.Number}
+   * @type {?ol.Transform}
    */
   this.imageTransformInv_ = null;
 
@@ -83,9 +82,8 @@ ol.renderer.canvas.ImageLayer.prototype.forEachLayerAtPixel = function(pixel, fr
   if (this.getLayer().getSource() instanceof ol.source.ImageVector) {
     // for ImageVector sources use the original hit-detection logic,
     // so that for example also transparent polygons are detected
-    var coordinate = pixel.slice();
-    ol.vec.Mat4.multVec2(
-        frameState.pixelToCoordinateMatrix, coordinate, coordinate);
+    var coordinate = ol.transform.apply(
+        frameState.pixelToCoordinateTransform, pixel.slice());
     var hasFeature = this.forEachFeatureAtCoordinate(
         coordinate, frameState, ol.functions.TRUE, this);
 
@@ -97,8 +95,7 @@ ol.renderer.canvas.ImageLayer.prototype.forEachLayerAtPixel = function(pixel, fr
   } else {
     // for all other image sources directly check the image
     if (!this.imageTransformInv_) {
-      this.imageTransformInv_ = goog.vec.Mat4.createNumber();
-      goog.vec.Mat4.invert(this.imageTransform_, this.imageTransformInv_);
+      this.imageTransformInv_ = ol.transform.invert(this.imageTransform_.slice());
     }
 
     var pixelOnCanvas =
@@ -190,11 +187,12 @@ ol.renderer.canvas.ImageLayer.prototype.prepareFrame = function(frameState, laye
     var imagePixelRatio = image.getPixelRatio();
     var scale = pixelRatio * imageResolution /
         (viewResolution * imagePixelRatio);
-    ol.vec.Mat4.makeTransform2D(this.imageTransform_,
+    var transform = ol.transform.reset(this.imageTransform_);
+    ol.transform.translate(transform,
         pixelRatio * frameState.size[0] / 2,
-        pixelRatio * frameState.size[1] / 2,
-        scale, scale,
-        0,
+        pixelRatio * frameState.size[1] / 2);
+    ol.transform.scale(transform, scale, scale);
+    ol.transform.translate(transform,
         imagePixelRatio * (imageExtent[0] - viewCenter[0]) / imageResolution,
         imagePixelRatio * (viewCenter[1] - imageExtent[3]) / imageResolution);
     this.imageTransformInv_ = null;
diff --git a/src/ol/renderer/canvas/canvaslayerrenderer.js b/src/ol/renderer/canvas/canvaslayerrenderer.js
index 852492ad4d..17a32158c1 100644
--- a/src/ol/renderer/canvas/canvaslayerrenderer.js
+++ b/src/ol/renderer/canvas/canvaslayerrenderer.js
@@ -1,7 +1,7 @@
 goog.provide('ol.renderer.canvas.Layer');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.extent');
 goog.require('ol.layer.Layer');
 goog.require('ol.render.Event');
@@ -9,7 +9,6 @@ goog.require('ol.render.EventType');
 goog.require('ol.render.canvas');
 goog.require('ol.render.canvas.Immediate');
 goog.require('ol.renderer.Layer');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -23,9 +22,9 @@ ol.renderer.canvas.Layer = function(layer) {
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.transform_ = goog.vec.Mat4.createNumber();
+  this.transform_ = ol.transform.create();
 
 };
 ol.inherits(ol.renderer.canvas.Layer, ol.renderer.Layer);
@@ -58,14 +57,10 @@ ol.renderer.canvas.Layer.prototype.composeFrame = function(frameState, layerStat
       var bottomRight = ol.extent.getBottomRight(extent);
       var bottomLeft = ol.extent.getBottomLeft(extent);
 
-      ol.vec.Mat4.multVec2(frameState.coordinateToPixelMatrix,
-          topLeft, topLeft);
-      ol.vec.Mat4.multVec2(frameState.coordinateToPixelMatrix,
-          topRight, topRight);
-      ol.vec.Mat4.multVec2(frameState.coordinateToPixelMatrix,
-          bottomRight, bottomRight);
-      ol.vec.Mat4.multVec2(frameState.coordinateToPixelMatrix,
-          bottomLeft, bottomLeft);
+      ol.transform.apply(frameState.coordinateToPixelTransform, topLeft);
+      ol.transform.apply(frameState.coordinateToPixelTransform, topRight);
+      ol.transform.apply(frameState.coordinateToPixelTransform, bottomRight);
+      ol.transform.apply(frameState.coordinateToPixelTransform, bottomLeft);
 
       context.save();
       ol.render.canvas.rotateAtOffset(context, -rotation, width / 2, height / 2);
@@ -87,10 +82,10 @@ ol.renderer.canvas.Layer.prototype.composeFrame = function(frameState, layerStat
 
     // for performance reasons, context.setTransform is only used
     // when the view is rotated. see http://jsperf.com/canvas-transform
-    var dx = goog.vec.Mat4.getElement(imageTransform, 0, 3);
-    var dy = goog.vec.Mat4.getElement(imageTransform, 1, 3);
-    var dw = image.width * goog.vec.Mat4.getElement(imageTransform, 0, 0);
-    var dh = image.height * goog.vec.Mat4.getElement(imageTransform, 1, 1);
+    var dx = imageTransform[4];
+    var dy = imageTransform[5];
+    var dw = image.width * imageTransform[0];
+    var dh = image.height * imageTransform[3];
     context.drawImage(image, 0, 0, +image.width, +image.height,
         Math.round(dx), Math.round(dy), Math.round(dw), Math.round(dh));
     context.globalAlpha = alpha;
@@ -109,7 +104,7 @@ ol.renderer.canvas.Layer.prototype.composeFrame = function(frameState, layerStat
  * @param {ol.render.EventType} type Event type.
  * @param {CanvasRenderingContext2D} context Context.
  * @param {olx.FrameState} frameState Frame state.
- * @param {goog.vec.Mat4.Number=} opt_transform Transform.
+ * @param {ol.Transform=} opt_transform Transform.
  * @private
  */
 ol.renderer.canvas.Layer.prototype.dispatchComposeEvent_ = function(type, context, frameState, opt_transform) {
@@ -135,7 +130,7 @@ ol.renderer.canvas.Layer.prototype.dispatchComposeEvent_ = function(type, contex
 /**
  * @param {CanvasRenderingContext2D} context Context.
  * @param {olx.FrameState} frameState Frame state.
- * @param {goog.vec.Mat4.Number=} opt_transform Transform.
+ * @param {ol.Transform=} opt_transform Transform.
  * @protected
  */
 ol.renderer.canvas.Layer.prototype.dispatchPostComposeEvent = function(context, frameState, opt_transform) {
@@ -147,7 +142,7 @@ ol.renderer.canvas.Layer.prototype.dispatchPostComposeEvent = function(context,
 /**
  * @param {CanvasRenderingContext2D} context Context.
  * @param {olx.FrameState} frameState Frame state.
- * @param {goog.vec.Mat4.Number=} opt_transform Transform.
+ * @param {ol.Transform=} opt_transform Transform.
  * @protected
  */
 ol.renderer.canvas.Layer.prototype.dispatchPreComposeEvent = function(context, frameState, opt_transform) {
@@ -159,7 +154,7 @@ ol.renderer.canvas.Layer.prototype.dispatchPreComposeEvent = function(context, f
 /**
  * @param {CanvasRenderingContext2D} context Context.
  * @param {olx.FrameState} frameState Frame state.
- * @param {goog.vec.Mat4.Number=} opt_transform Transform.
+ * @param {ol.Transform=} opt_transform Transform.
  * @protected
  */
 ol.renderer.canvas.Layer.prototype.dispatchRenderEvent = function(context, frameState, opt_transform) {
@@ -175,7 +170,7 @@ ol.renderer.canvas.Layer.prototype.getImage = goog.abstractMethod;
 
 
 /**
- * @return {!goog.vec.Mat4.Number} Image transform.
+ * @return {!ol.Transform} Image transform.
  */
 ol.renderer.canvas.Layer.prototype.getImageTransform = goog.abstractMethod;
 
@@ -184,19 +179,19 @@ ol.renderer.canvas.Layer.prototype.getImageTransform = goog.abstractMethod;
  * @param {olx.FrameState} frameState Frame state.
  * @param {number} offsetX Offset on the x-axis in view coordinates.
  * @protected
- * @return {!goog.vec.Mat4.Number} Transform.
+ * @return {!ol.Transform} Transform.
  */
 ol.renderer.canvas.Layer.prototype.getTransform = function(frameState, offsetX) {
   var viewState = frameState.viewState;
   var pixelRatio = frameState.pixelRatio;
-  return ol.vec.Mat4.makeTransform2D(this.transform_,
-      pixelRatio * frameState.size[0] / 2,
-      pixelRatio * frameState.size[1] / 2,
-      pixelRatio / viewState.resolution,
-      -pixelRatio / viewState.resolution,
-      -viewState.rotation,
-      -viewState.center[0] + offsetX,
-      -viewState.center[1]);
+  var dx1 = pixelRatio * frameState.size[0] / 2;
+  var dy1 = pixelRatio * frameState.size[1] / 2;
+  var sx = pixelRatio / viewState.resolution;
+  var sy = -sx;
+  var angle = -viewState.rotation;
+  var dx2 = -viewState.center[0] + offsetX;
+  var dy2 = -viewState.center[1];
+  return ol.transform.compose(this.transform_, dx1, dy1, sx, sy, angle, dx2, dy2);
 };
 
 
@@ -210,13 +205,11 @@ ol.renderer.canvas.Layer.prototype.prepareFrame = goog.abstractMethod;
 
 /**
  * @param {ol.Pixel} pixelOnMap Pixel.
- * @param {goog.vec.Mat4.Number} imageTransformInv The transformation matrix
+ * @param {ol.Transform} imageTransformInv The transformation matrix
  *        to convert from a map pixel to a canvas pixel.
  * @return {ol.Pixel} The pixel.
  * @protected
  */
 ol.renderer.canvas.Layer.prototype.getPixelOnCanvas = function(pixelOnMap, imageTransformInv) {
-  var pixelOnCanvas = [0, 0];
-  ol.vec.Mat4.multVec2(imageTransformInv, pixelOnMap, pixelOnCanvas);
-  return pixelOnCanvas;
+  return ol.transform.apply(imageTransformInv, pixelOnMap.slice());
 };
diff --git a/src/ol/renderer/canvas/canvasmaprenderer.js b/src/ol/renderer/canvas/canvasmaprenderer.js
index 7c8f599047..9aff0c3daf 100644
--- a/src/ol/renderer/canvas/canvasmaprenderer.js
+++ b/src/ol/renderer/canvas/canvasmaprenderer.js
@@ -3,7 +3,7 @@
 goog.provide('ol.renderer.canvas.Map');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol');
 goog.require('ol.RendererType');
 goog.require('ol.array');
@@ -25,7 +25,6 @@ goog.require('ol.renderer.canvas.TileLayer');
 goog.require('ol.renderer.canvas.VectorLayer');
 goog.require('ol.renderer.canvas.VectorTileLayer');
 goog.require('ol.source.State');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -63,9 +62,9 @@ ol.renderer.canvas.Map = function(container, map) {
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.transform_ = goog.vec.Mat4.createNumber();
+  this.transform_ = ol.transform.create();
 
 };
 ol.inherits(ol.renderer.canvas.Map, ol.renderer.Map);
@@ -118,17 +117,18 @@ ol.renderer.canvas.Map.prototype.dispatchComposeEvent_ = function(type, frameSta
 /**
  * @param {olx.FrameState} frameState Frame state.
  * @protected
- * @return {!goog.vec.Mat4.Number} Transform.
+ * @return {!ol.Transform} Transform.
  */
 ol.renderer.canvas.Map.prototype.getTransform = function(frameState) {
-  var pixelRatio = frameState.pixelRatio;
   var viewState = frameState.viewState;
-  var resolution = viewState.resolution;
-  return ol.vec.Mat4.makeTransform2D(this.transform_,
-      this.canvas_.width / 2, this.canvas_.height / 2,
-      pixelRatio / resolution, -pixelRatio / resolution,
-      -viewState.rotation,
-      -viewState.center[0], -viewState.center[1]);
+  var dx1 = this.canvas_.width / 2;
+  var dy1 = this.canvas_.height / 2;
+  var sx = frameState.pixelRatio / viewState.resolution;
+  var sy = -sx;
+  var angle = -viewState.rotation;
+  var dx2 = -viewState.center[0];
+  var dy2 = -viewState.center[1];
+  return ol.transform.compose(this.transform_, dx1, dy1, sx, sy, angle, dx2, dy2);
 };
 
 
diff --git a/src/ol/renderer/canvas/canvastilelayerrenderer.js b/src/ol/renderer/canvas/canvastilelayerrenderer.js
index 1d7f2c812b..01d6f14f03 100644
--- a/src/ol/renderer/canvas/canvastilelayerrenderer.js
+++ b/src/ol/renderer/canvas/canvastilelayerrenderer.js
@@ -3,7 +3,7 @@
 goog.provide('ol.renderer.canvas.TileLayer');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.TileRange');
 goog.require('ol.TileState');
 goog.require('ol.array');
@@ -13,7 +13,6 @@ goog.require('ol.render.EventType');
 goog.require('ol.renderer.canvas.Layer');
 goog.require('ol.size');
 goog.require('ol.source.Tile');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -51,9 +50,9 @@ ol.renderer.canvas.TileLayer = function(tileLayer) {
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.imageTransform_ = goog.vec.Mat4.createNumber();
+  this.imageTransform_ = ol.transform.create();
 
   /**
    * @protected
@@ -366,9 +365,11 @@ ol.renderer.canvas.TileLayer.prototype.renderTileImages = function(context, fram
   if (hasRenderListeners) {
     var dX = drawOffsetX - offsetX / drawScale + offsetX;
     var dY = drawOffsetY - offsetY / drawScale + offsetY;
-    var imageTransform = ol.vec.Mat4.makeTransform2D(this.imageTransform_,
-        drawSize / 2 - dX, drawSize / 2 - dY, pixelScale, -pixelScale,
-        -rotation, -center[0] + dX / pixelScale, -center[1] - dY / pixelScale);
+    var imageTransform = ol.transform.compose(this.imageTransform_,
+        drawSize / 2 - dX, drawSize / 2 - dY,
+        pixelScale, -pixelScale,
+        -rotation,
+        -center[0] + dX / pixelScale, -center[1] - dY / pixelScale);
     this.dispatchRenderEvent(renderContext, frameState, imageTransform);
   }
   if (rotation || hasRenderListeners) {
diff --git a/src/ol/renderer/canvas/canvasvectortilelayerrenderer.js b/src/ol/renderer/canvas/canvasvectortilelayerrenderer.js
index 56ea0cfe82..d073d947b2 100644
--- a/src/ol/renderer/canvas/canvasvectortilelayerrenderer.js
+++ b/src/ol/renderer/canvas/canvasvectortilelayerrenderer.js
@@ -2,7 +2,7 @@ goog.provide('ol.renderer.canvas.VectorTileLayer');
 
 goog.require('goog.asserts');
 goog.require('ol.events');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.Feature');
 goog.require('ol.VectorTile');
 goog.require('ol.array');
@@ -17,7 +17,6 @@ goog.require('ol.renderer.canvas.TileLayer');
 goog.require('ol.renderer.vector');
 goog.require('ol.size');
 goog.require('ol.source.VectorTile');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -57,9 +56,9 @@ ol.renderer.canvas.VectorTileLayer = function(layer) {
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.tmpTransform_ = goog.vec.Mat4.createNumber();
+  this.tmpTransform_ = ol.transform.create();
 
   // Use lower resolution for pure vector rendering. Closest resolution otherwise.
   this.zDirection =
@@ -148,13 +147,12 @@ ol.renderer.canvas.VectorTileLayer.prototype.renderTileReplays_ = function(
 
     if (pixelSpace) {
       origin = ol.extent.getTopLeft(tileExtent);
-      tileTransform = ol.vec.Mat4.makeTransform2D(this.tmpTransform_,
+      tileTransform = ol.transform.reset(this.tmpTransform_);
+      tileTransform = ol.transform.compose(this.tmpTransform_,
           offsetX, offsetY,
-          pixelScale * tilePixelResolution,
-          pixelScale * tilePixelResolution,
+          pixelScale * tilePixelResolution, pixelScale * tilePixelResolution,
           rotation,
-          (origin[0] - center[0]) / tilePixelResolution,
-          (center[1] - origin[1]) / tilePixelResolution);
+          (origin[0] - center[0]) / tilePixelResolution, (center[1] - origin[1]) / tilePixelResolution);
     } else {
       tileTransform = transform;
     }
@@ -426,20 +424,16 @@ ol.renderer.canvas.VectorTileLayer.prototype.renderTileImage_ = function(
     var tilePixelResolution = tileResolution / tilePixelRatio;
     var tileExtent = tileGrid.getTileCoordExtent(
         tile.getTileCoord(), this.tmpExtent);
-    var tileTransform;
+    var tileTransform = ol.transform.reset(this.tmpTransform_);
     if (pixelSpace) {
-      tileTransform = ol.vec.Mat4.makeTransform2D(this.tmpTransform_,
-          0, 0,
-          pixelScale * tilePixelResolution, pixelScale * tilePixelResolution,
-          0,
+      ol.transform.scale(tileTransform,
+          pixelScale * tilePixelResolution, pixelScale * tilePixelResolution);
+      ol.transform.translate(tileTransform,
           -tileSize[0] * tilePixelRatio / 2, -tileSize[1] * tilePixelRatio / 2);
     } else {
       var tileCenter = ol.extent.getCenter(tileExtent);
-      tileTransform = ol.vec.Mat4.makeTransform2D(this.tmpTransform_,
-          0, 0,
-          pixelScale, -pixelScale,
-          0,
-          -tileCenter[0], -tileCenter[1]);
+      ol.transform.scale(tileTransform, pixelScale, -pixelScale);
+      ol.transform.translate(tileTransform, -tileCenter[0], -tileCenter[1]);
     }
 
     replayState.replayGroup.replay(tileContext, pixelRatio,
diff --git a/src/ol/renderer/dom/domimagelayerrenderer.js b/src/ol/renderer/dom/domimagelayerrenderer.js
index a0d1a931c5..791fe354e0 100644
--- a/src/ol/renderer/dom/domimagelayerrenderer.js
+++ b/src/ol/renderer/dom/domimagelayerrenderer.js
@@ -1,7 +1,7 @@
 goog.provide('ol.renderer.dom.ImageLayer');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.ImageBase');
 goog.require('ol.ViewHint');
 goog.require('ol.dom');
@@ -9,7 +9,6 @@ goog.require('ol.extent');
 goog.require('ol.layer.Image');
 goog.require('ol.proj');
 goog.require('ol.renderer.dom.Layer');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -32,9 +31,9 @@ ol.renderer.dom.ImageLayer = function(imageLayer) {
 
   /**
    * @private
-   * @type {goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.transform_ = goog.vec.Mat4.createNumberIdentity();
+  this.transform_ = ol.transform.create();
 
 };
 ol.inherits(ol.renderer.dom.ImageLayer, ol.renderer.dom.Layer);
@@ -118,13 +117,14 @@ ol.renderer.dom.ImageLayer.prototype.prepareFrame = function(frameState, layerSt
   if (image) {
     var imageExtent = image.getExtent();
     var imageResolution = image.getResolution();
-    var transform = goog.vec.Mat4.createNumber();
-    ol.vec.Mat4.makeTransform2D(transform,
+    var transform = ol.transform.create();
+    ol.transform.compose(transform,
         frameState.size[0] / 2, frameState.size[1] / 2,
         imageResolution / viewResolution, imageResolution / viewResolution,
         viewRotation,
         (imageExtent[0] - viewCenter[0]) / imageResolution,
         (viewCenter[1] - imageExtent[3]) / imageResolution);
+
     if (image != this.image_) {
       var imageElement = image.getImage(this);
       // Bootstrap sets the style max-width: 100% for all images, which breaks
@@ -146,12 +146,12 @@ ol.renderer.dom.ImageLayer.prototype.prepareFrame = function(frameState, layerSt
 
 
 /**
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @private
  */
 ol.renderer.dom.ImageLayer.prototype.setTransform_ = function(transform) {
-  if (!ol.vec.Mat4.equals2D(transform, this.transform_)) {
+  if (!ol.array.equals(transform, this.transform_)) {
     ol.dom.transformElement2D(this.target, transform, 6);
-    goog.vec.Mat4.setFromArray(this.transform_, transform);
+    ol.transform.setFromArray(this.transform_, transform);
   }
 };
diff --git a/src/ol/renderer/dom/dommaprenderer.js b/src/ol/renderer/dom/dommaprenderer.js
index c6cf82d1bc..2571104e2e 100644
--- a/src/ol/renderer/dom/dommaprenderer.js
+++ b/src/ol/renderer/dom/dommaprenderer.js
@@ -4,7 +4,7 @@ goog.require('goog.asserts');
 goog.require('ol.events');
 goog.require('ol.events.Event');
 goog.require('ol.events.EventType');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol');
 goog.require('ol.RendererType');
 goog.require('ol.array');
@@ -23,7 +23,6 @@ goog.require('ol.renderer.dom.Layer');
 goog.require('ol.renderer.dom.TileLayer');
 goog.require('ol.renderer.dom.VectorLayer');
 goog.require('ol.source.State');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -50,9 +49,9 @@ ol.renderer.dom.Map = function(container, map) {
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.transform_ = goog.vec.Mat4.createNumber();
+  this.transform_ = ol.transform.create();
 
   /**
    * @type {!Element}
@@ -124,15 +123,14 @@ ol.renderer.dom.Map.prototype.dispatchComposeEvent_ = function(type, frameState)
     var context = this.context_;
     var canvas = context.canvas;
 
-    ol.vec.Mat4.makeTransform2D(this.transform_,
-        canvas.width / 2,
-        canvas.height / 2,
-        pixelRatio / viewState.resolution,
-        -pixelRatio / viewState.resolution,
-        -viewState.rotation,
+    var transform = ol.transform.compose(this.transform_,
+        canvas.width / 2, canvas.height / 2,
+        pixelRatio / viewState.resolution, -pixelRatio / viewState.resolution,
+        -rotation,
         -viewState.center[0], -viewState.center[1]);
+
     var vectorContext = new ol.render.canvas.Immediate(context, pixelRatio,
-        extent, this.transform_, rotation);
+        extent, transform, rotation);
     var composeEvent = new ol.render.Event(type, map, vectorContext,
         frameState, context, null);
     map.dispatchEvent(composeEvent);
diff --git a/src/ol/renderer/dom/domtilelayerrenderer.js b/src/ol/renderer/dom/domtilelayerrenderer.js
index 4797c5cc94..3bf9b7914d 100644
--- a/src/ol/renderer/dom/domtilelayerrenderer.js
+++ b/src/ol/renderer/dom/domtilelayerrenderer.js
@@ -4,7 +4,7 @@
 goog.provide('ol.renderer.dom.TileLayer');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol');
 goog.require('ol.TileRange');
 goog.require('ol.TileState');
@@ -16,7 +16,6 @@ goog.require('ol.layer.Tile');
 goog.require('ol.renderer.dom.Layer');
 goog.require('ol.size');
 goog.require('ol.tilegrid.TileGrid');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -200,7 +199,7 @@ ol.renderer.dom.TileLayer.prototype.prepareFrame = function(frameState, layerSta
   tileLayerZKeys.sort(ol.array.numberSafeCompareFunction);
 
   var i, ii, j, origin, resolution;
-  var transform = goog.vec.Mat4.createNumber();
+  var transform = ol.transform.create();
   for (i = 0, ii = tileLayerZKeys.length; i < ii; ++i) {
     tileLayerZKey = tileLayerZKeys[i];
     tileLayerZ = this.tileLayerZs_[tileLayerZKey];
@@ -211,13 +210,13 @@ ol.renderer.dom.TileLayer.prototype.prepareFrame = function(frameState, layerSta
     }
     resolution = tileLayerZ.getResolution();
     origin = tileLayerZ.getOrigin();
-    ol.vec.Mat4.makeTransform2D(transform,
+
+    ol.transform.compose(transform,
         frameState.size[0] / 2, frameState.size[1] / 2,
-        resolution / viewState.resolution,
-        resolution / viewState.resolution,
+        resolution / viewState.resolution, resolution / viewState.resolution,
         viewState.rotation,
-        (origin[0] - center[0]) / resolution,
-        (center[1] - origin[1]) / resolution);
+        (origin[0] - center[0]) / resolution, (center[1] - origin[1]) / resolution);
+
     tileLayerZ.setTransform(transform);
     if (tileLayerZKey in newTileLayerZKeys) {
       for (j = tileLayerZKey - 1; j >= 0; --j) {
@@ -314,9 +313,9 @@ ol.renderer.dom.TileLayerZ_ = function(tileGrid, tileCoordOrigin) {
 
   /**
    * @private
-   * @type {goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.transform_ = goog.vec.Mat4.createNumberIdentity();
+  this.transform_ = ol.transform.create();
 
   /**
    * @private
@@ -437,11 +436,11 @@ ol.renderer.dom.TileLayerZ_.prototype.removeTilesOutsideExtent = function(extent
 
 
 /**
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  */
 ol.renderer.dom.TileLayerZ_.prototype.setTransform = function(transform) {
-  if (!ol.vec.Mat4.equals2D(transform, this.transform_)) {
+  if (!ol.array.equals(transform, this.transform_)) {
     ol.dom.transformElement2D(this.target, transform, 6);
-    goog.vec.Mat4.setFromArray(this.transform_, transform);
+    ol.transform.setFromArray(this.transform_, transform);
   }
 };
diff --git a/src/ol/renderer/dom/domvectorlayerrenderer.js b/src/ol/renderer/dom/domvectorlayerrenderer.js
index 116de9bc94..5f4d0acff4 100644
--- a/src/ol/renderer/dom/domvectorlayerrenderer.js
+++ b/src/ol/renderer/dom/domvectorlayerrenderer.js
@@ -2,7 +2,7 @@ goog.provide('ol.renderer.dom.VectorLayer');
 
 goog.require('goog.asserts');
 goog.require('ol.events');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.ViewHint');
 goog.require('ol.dom');
 goog.require('ol.extent');
@@ -13,7 +13,6 @@ goog.require('ol.render.canvas.Immediate');
 goog.require('ol.render.canvas.ReplayGroup');
 goog.require('ol.renderer.dom.Layer');
 goog.require('ol.renderer.vector');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -76,15 +75,15 @@ ol.renderer.dom.VectorLayer = function(vectorLayer) {
 
   /**
    * @private
-   * @type {goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.transform_ = goog.vec.Mat4.createNumber();
+  this.transform_ = ol.transform.create();
 
   /**
    * @private
-   * @type {goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.elementTransform_ = goog.vec.Mat4.createNumber();
+  this.elementTransform_ = ol.transform.create();
 
 };
 ol.inherits(ol.renderer.dom.VectorLayer, ol.renderer.dom.Layer);
@@ -120,11 +119,9 @@ ol.renderer.dom.VectorLayer.prototype.composeFrame = function(frameState, layerS
   var imageWidth = viewWidth * pixelRatio;
   var imageHeight = viewHeight * pixelRatio;
 
-  var transform = ol.vec.Mat4.makeTransform2D(this.transform_,
-      pixelRatio * viewWidth / 2,
-      pixelRatio * viewHeight / 2,
-      pixelRatio / viewResolution,
-      -pixelRatio / viewResolution,
+  var transform = ol.transform.compose(this.transform_,
+      pixelRatio * viewWidth / 2, pixelRatio * viewHeight / 2,
+      pixelRatio / viewResolution, -pixelRatio / viewResolution,
       -viewRotation,
       -viewCenter[0], -viewCenter[1]);
 
@@ -134,10 +131,9 @@ ol.renderer.dom.VectorLayer.prototype.composeFrame = function(frameState, layerS
   context.canvas.width = imageWidth;
   context.canvas.height = imageHeight;
 
-  var elementTransform = ol.vec.Mat4.makeTransform2D(this.elementTransform_,
-      0, 0,
-      1 / pixelRatio, 1 / pixelRatio,
-      0,
+  var elementTransform = ol.transform.reset(this.elementTransform_);
+  ol.transform.scale(elementTransform, 1 / pixelRatio, 1 / pixelRatio);
+  ol.transform.translate(elementTransform,
       -(imageWidth - viewWidth) / 2 * pixelRatio,
       -(imageHeight - viewHeight) / 2 * pixelRatio);
   ol.dom.transformElement2D(context.canvas, elementTransform, 6);
@@ -162,7 +158,7 @@ ol.renderer.dom.VectorLayer.prototype.composeFrame = function(frameState, layerS
 /**
  * @param {ol.render.EventType} type Event type.
  * @param {olx.FrameState} frameState Frame state.
- * @param {goog.vec.Mat4.Number} transform Transform.
+ * @param {ol.Transform} transform Transform.
  * @private
  */
 ol.renderer.dom.VectorLayer.prototype.dispatchEvent_ = function(type, frameState, transform) {
diff --git a/src/ol/renderer/layerrenderer.js b/src/ol/renderer/layerrenderer.js
index e8eaea77c5..6a0d980d63 100644
--- a/src/ol/renderer/layerrenderer.js
+++ b/src/ol/renderer/layerrenderer.js
@@ -10,10 +10,9 @@ goog.require('ol.Observable');
 goog.require('ol.TileRange');
 goog.require('ol.TileState');
 goog.require('ol.layer.Layer');
-goog.require('ol.source.Source');
+goog.require('ol.transform');
 goog.require('ol.source.State');
 goog.require('ol.source.Tile');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -58,9 +57,8 @@ ol.renderer.Layer.prototype.forEachFeatureAtCoordinate = ol.nullFunction;
  * @template S,T
  */
 ol.renderer.Layer.prototype.forEachLayerAtPixel = function(pixel, frameState, callback, thisArg) {
-  var coordinate = pixel.slice();
-  ol.vec.Mat4.multVec2(
-      frameState.pixelToCoordinateMatrix, coordinate, coordinate);
+  var coordinate = ol.transform.apply(
+      frameState.pixelToCoordinateTransform, pixel.slice());
 
   var hasFeature = this.forEachFeatureAtCoordinate(
       coordinate, frameState, ol.functions.TRUE, this);
diff --git a/src/ol/renderer/maprenderer.js b/src/ol/renderer/maprenderer.js
index 38c131a593..98d8c2580f 100644
--- a/src/ol/renderer/maprenderer.js
+++ b/src/ol/renderer/maprenderer.js
@@ -2,7 +2,7 @@ goog.provide('ol.RendererType');
 goog.provide('ol.renderer.Map');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol');
 goog.require('ol.Disposable');
 goog.require('ol.events');
@@ -12,7 +12,6 @@ goog.require('ol.functions');
 goog.require('ol.layer.Layer');
 goog.require('ol.renderer.Layer');
 goog.require('ol.style.IconImageCache');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -66,17 +65,19 @@ ol.inherits(ol.renderer.Map, ol.Disposable);
  */
 ol.renderer.Map.prototype.calculateMatrices2D = function(frameState) {
   var viewState = frameState.viewState;
-  var coordinateToPixelMatrix = frameState.coordinateToPixelMatrix;
-  goog.asserts.assert(coordinateToPixelMatrix,
-      'frameState has a coordinateToPixelMatrix');
-  ol.vec.Mat4.makeTransform2D(coordinateToPixelMatrix,
+  var coordinateToPixelTransform = frameState.coordinateToPixelTransform;
+  var pixelToCoordinateTransform = frameState.pixelToCoordinateTransform;
+  goog.asserts.assert(coordinateToPixelTransform,
+      'frameState has a coordinateToPixelTransform');
+
+  ol.transform.compose(coordinateToPixelTransform,
       frameState.size[0] / 2, frameState.size[1] / 2,
       1 / viewState.resolution, -1 / viewState.resolution,
       -viewState.rotation,
       -viewState.center[0], -viewState.center[1]);
-  var inverted = goog.vec.Mat4.invert(
-      coordinateToPixelMatrix, frameState.pixelToCoordinateMatrix);
-  goog.asserts.assert(inverted, 'matrix could be inverted');
+
+  ol.transform.invert(
+      ol.transform.setFromArray(pixelToCoordinateTransform, coordinateToPixelTransform));
 };
 
 
diff --git a/src/ol/renderer/webgl/webglimagelayerrenderer.js b/src/ol/renderer/webgl/webglimagelayerrenderer.js
index afe4641703..cc57c79bb7 100644
--- a/src/ol/renderer/webgl/webglimagelayerrenderer.js
+++ b/src/ol/renderer/webgl/webglimagelayerrenderer.js
@@ -1,7 +1,7 @@
 goog.provide('ol.renderer.webgl.ImageLayer');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('goog.webgl');
 goog.require('ol.ImageBase');
 goog.require('ol.ViewHint');
@@ -12,7 +12,6 @@ goog.require('ol.layer.Image');
 goog.require('ol.proj');
 goog.require('ol.renderer.webgl.Layer');
 goog.require('ol.source.ImageVector');
-goog.require('ol.vec.Mat4');
 goog.require('ol.webgl.Context');
 
 
@@ -41,7 +40,7 @@ ol.renderer.webgl.ImageLayer = function(mapRenderer, imageLayer) {
 
   /**
    * @private
-   * @type {?goog.vec.Mat4.Number}
+   * @type {?ol.Transform}
    */
   this.hitTransformationMatrix_ = null;
 
@@ -165,9 +164,9 @@ ol.renderer.webgl.ImageLayer.prototype.prepareFrame = function(frameState, layer
 
     // Translate and scale to flip the Y coord.
     var texCoordMatrix = this.texCoordMatrix;
-    goog.vec.Mat4.makeIdentity(texCoordMatrix);
-    goog.vec.Mat4.scale(texCoordMatrix, 1, -1, 1);
-    goog.vec.Mat4.translate(texCoordMatrix, 0, -1, 0);
+    ol.transform.reset(texCoordMatrix);
+    ol.transform.scale(texCoordMatrix, 1, -1);
+    ol.transform.translate(texCoordMatrix, 0, -1);
 
     this.image_ = image;
     this.texture = texture;
@@ -197,20 +196,18 @@ ol.renderer.webgl.ImageLayer.prototype.updateProjectionMatrix_ = function(canvas
   var canvasExtentHeight = canvasHeight * viewResolution;
 
   var projectionMatrix = this.projectionMatrix;
-  goog.vec.Mat4.makeIdentity(projectionMatrix);
-  goog.vec.Mat4.scale(projectionMatrix,
+  ol.transform.reset(projectionMatrix);
+  ol.transform.scale(projectionMatrix,
       pixelRatio * 2 / canvasExtentWidth,
-      pixelRatio * 2 / canvasExtentHeight, 1);
-  goog.vec.Mat4.rotateZ(projectionMatrix, -viewRotation);
-  goog.vec.Mat4.translate(projectionMatrix,
+      pixelRatio * 2 / canvasExtentHeight);
+  ol.transform.rotate(projectionMatrix, -viewRotation);
+  ol.transform.translate(projectionMatrix,
       imageExtent[0] - viewCenter[0],
-      imageExtent[1] - viewCenter[1],
-      0);
-  goog.vec.Mat4.scale(projectionMatrix,
+      imageExtent[1] - viewCenter[1]);
+  ol.transform.scale(projectionMatrix,
       (imageExtent[2] - imageExtent[0]) / 2,
-      (imageExtent[3] - imageExtent[1]) / 2,
-      1);
-  goog.vec.Mat4.translate(projectionMatrix, 1, 1, 0);
+      (imageExtent[3] - imageExtent[1]) / 2);
+  ol.transform.translate(projectionMatrix, 1, 1);
 
 };
 
@@ -236,9 +233,8 @@ ol.renderer.webgl.ImageLayer.prototype.forEachLayerAtPixel = function(pixel, fra
   if (this.getLayer().getSource() instanceof ol.source.ImageVector) {
     // for ImageVector sources use the original hit-detection logic,
     // so that for example also transparent polygons are detected
-    var coordinate = pixel.slice();
-    ol.vec.Mat4.multVec2(
-        frameState.pixelToCoordinateMatrix, coordinate, coordinate);
+    var coordinate = ol.transform.apply(
+        frameState.pixelToCoordinateTransform, pixel.slice());
     var hasFeature = this.forEachFeatureAtCoordinate(
         coordinate, frameState, ol.functions.TRUE, this);
 
@@ -256,9 +252,8 @@ ol.renderer.webgl.ImageLayer.prototype.forEachLayerAtPixel = function(pixel, fra
           frameState.size, imageSize);
     }
 
-    var pixelOnFrameBuffer = [0, 0];
-    ol.vec.Mat4.multVec2(
-        this.hitTransformationMatrix_, pixel, pixelOnFrameBuffer);
+    var pixelOnFrameBuffer = ol.transform.apply(
+        this.hitTransformationMatrix_, pixel.slice());
 
     if (pixelOnFrameBuffer[0] < 0 || pixelOnFrameBuffer[0] > imageSize[0] ||
         pixelOnFrameBuffer[1] < 0 || pixelOnFrameBuffer[1] > imageSize[1]) {
@@ -289,37 +284,31 @@ ol.renderer.webgl.ImageLayer.prototype.forEachLayerAtPixel = function(pixel, fra
  * pixel on the map.
  * @param {ol.Size} mapSize The map size.
  * @param {ol.Size} imageSize The image size.
- * @return {goog.vec.Mat4.Number} The transformation matrix.
+ * @return {ol.Transform} The transformation matrix.
  * @private
  */
 ol.renderer.webgl.ImageLayer.prototype.getHitTransformationMatrix_ = function(mapSize, imageSize) {
   // the first matrix takes a map pixel, flips the y-axis and scales to
   // a range between -1 ... 1
-  var mapCoordMatrix = goog.vec.Mat4.createNumber();
-  goog.vec.Mat4.makeIdentity(mapCoordMatrix);
-  goog.vec.Mat4.translate(mapCoordMatrix, -1, -1, 0);
-  goog.vec.Mat4.scale(mapCoordMatrix, 2 / mapSize[0], 2 / mapSize[1], 1);
-  goog.vec.Mat4.translate(mapCoordMatrix, 0, mapSize[1], 0);
-  goog.vec.Mat4.scale(mapCoordMatrix, 1, -1, 1);
+  var mapCoordTransform = ol.transform.create();
+  ol.transform.translate(mapCoordTransform, -1, -1);
+  ol.transform.scale(mapCoordTransform, 2 / mapSize[0], 2 / mapSize[1]);
+  ol.transform.translate(mapCoordTransform, 0, mapSize[1]);
+  ol.transform.scale(mapCoordTransform, 1, -1);
 
   // the second matrix is the inverse of the projection matrix used in the
   // shader for drawing
-  var projectionMatrixInv = goog.vec.Mat4.createNumber();
-  goog.vec.Mat4.invert(this.projectionMatrix, projectionMatrixInv);
+  var projectionMatrixInv = ol.transform.invert(this.projectionMatrix.slice());
 
   // the third matrix scales to the image dimensions and flips the y-axis again
-  var imageCoordMatrix = goog.vec.Mat4.createNumber();
-  goog.vec.Mat4.makeIdentity(imageCoordMatrix);
-  goog.vec.Mat4.translate(imageCoordMatrix, 0, imageSize[1], 0);
-  goog.vec.Mat4.scale(imageCoordMatrix, 1, -1, 1);
-  goog.vec.Mat4.scale(imageCoordMatrix, imageSize[0] / 2, imageSize[1] / 2, 1);
-  goog.vec.Mat4.translate(imageCoordMatrix, 1, 1, 0);
+  var transform = ol.transform.create();
+  ol.transform.translate(transform, 0, imageSize[1]);
+  ol.transform.scale(transform, 1, -1);
+  ol.transform.scale(transform, imageSize[0] / 2, imageSize[1] / 2);
+  ol.transform.translate(transform, 1, 1);
 
-  var transformMatrix = goog.vec.Mat4.createNumber();
-  goog.vec.Mat4.multMat(
-      imageCoordMatrix, projectionMatrixInv, transformMatrix);
-  goog.vec.Mat4.multMat(
-      transformMatrix, mapCoordMatrix, transformMatrix);
+  ol.transform.multiply(transform, projectionMatrixInv);
+  ol.transform.multiply(transform, mapCoordTransform);
 
-  return transformMatrix;
+  return transform;
 };
diff --git a/src/ol/renderer/webgl/webgllayerrenderer.js b/src/ol/renderer/webgl/webgllayerrenderer.js
index 16734822f1..03f220cc3f 100644
--- a/src/ol/renderer/webgl/webgllayerrenderer.js
+++ b/src/ol/renderer/webgl/webgllayerrenderer.js
@@ -1,8 +1,8 @@
 goog.provide('ol.renderer.webgl.Layer');
 
-goog.require('goog.vec.Mat4');
 goog.require('goog.webgl');
 goog.require('ol.layer.Layer');
+goog.require('ol.transform');
 goog.require('ol.render.Event');
 goog.require('ol.render.EventType');
 goog.require('ol.render.webgl.Immediate');
@@ -11,6 +11,7 @@ goog.require('ol.renderer.webgl.map.shader.Default');
 goog.require('ol.renderer.webgl.map.shader.Default.Locations');
 goog.require('ol.renderer.webgl.map.shader.DefaultFragment');
 goog.require('ol.renderer.webgl.map.shader.DefaultVertex');
+goog.require('ol.vec.Mat4');
 goog.require('ol.webgl.Buffer');
 goog.require('ol.webgl.Context');
 
@@ -62,15 +63,21 @@ ol.renderer.webgl.Layer = function(mapRenderer, layer) {
 
   /**
    * @protected
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.texCoordMatrix = goog.vec.Mat4.createNumber();
+  this.texCoordMatrix = ol.transform.create();
 
   /**
    * @protected
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.projectionMatrix = goog.vec.Mat4.createNumberIdentity();
+  this.projectionMatrix = ol.transform.create();
+
+  /**
+   * @type {Array.<number>}
+   * @private
+   */
+  this.tmpMat4_ = ol.vec.Mat4.create();
 
   /**
    * @private
@@ -167,10 +174,10 @@ ol.renderer.webgl.Layer.prototype.composeFrame = function(frameState, layerState
     gl.uniform1i(locations.u_texture, 0);
   }
 
-  gl.uniformMatrix4fv(
-      locations.u_texCoordMatrix, false, this.getTexCoordMatrix());
+  gl.uniformMatrix4fv(locations.u_texCoordMatrix, false,
+      ol.vec.Mat4.fromTransform(this.tmpMat4_, this.getTexCoordMatrix()));
   gl.uniformMatrix4fv(locations.u_projectionMatrix, false,
-      this.getProjectionMatrix());
+      ol.vec.Mat4.fromTransform(this.tmpMat4_, this.getProjectionMatrix()));
   gl.uniform1f(locations.u_opacity, layerState.opacity);
   gl.bindTexture(goog.webgl.TEXTURE_2D, this.getTexture());
   gl.drawArrays(goog.webgl.TRIANGLE_STRIP, 0, 4);
@@ -208,7 +215,7 @@ ol.renderer.webgl.Layer.prototype.dispatchComposeEvent_ = function(type, context
 
 
 /**
- * @return {!goog.vec.Mat4.Number} Matrix.
+ * @return {!ol.Transform} Matrix.
  */
 ol.renderer.webgl.Layer.prototype.getTexCoordMatrix = function() {
   return this.texCoordMatrix;
@@ -224,7 +231,7 @@ ol.renderer.webgl.Layer.prototype.getTexture = function() {
 
 
 /**
- * @return {!goog.vec.Mat4.Number} Matrix.
+ * @return {!ol.Transform} Matrix.
  */
 ol.renderer.webgl.Layer.prototype.getProjectionMatrix = function() {
   return this.projectionMatrix;
diff --git a/src/ol/renderer/webgl/webgltilelayerrenderer.js b/src/ol/renderer/webgl/webgltilelayerrenderer.js
index 407a18d184..3a8dcee8c1 100644
--- a/src/ol/renderer/webgl/webgltilelayerrenderer.js
+++ b/src/ol/renderer/webgl/webgltilelayerrenderer.js
@@ -4,8 +4,7 @@
 goog.provide('ol.renderer.webgl.TileLayer');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
-goog.require('goog.vec.Vec4');
+goog.require('ol.transform');
 goog.require('goog.webgl');
 goog.require('ol.TileRange');
 goog.require('ol.TileState');
@@ -18,7 +17,6 @@ goog.require('ol.renderer.webgl.tilelayer.shader.Fragment');
 goog.require('ol.renderer.webgl.tilelayer.shader.Locations');
 goog.require('ol.renderer.webgl.tilelayer.shader.Vertex');
 goog.require('ol.size');
-goog.require('ol.vec.Mat4');
 goog.require('ol.webgl.Buffer');
 
 
@@ -294,22 +292,21 @@ ol.renderer.webgl.TileLayer.prototype.prepareFrame = function(frameState, layerS
     /** @type {Array.<number>} */
     var zs = Object.keys(tilesToDrawByZ).map(Number);
     zs.sort(ol.array.numberSafeCompareFunction);
-    var u_tileOffset = goog.vec.Vec4.createFloat32();
-    var i, ii, sx, sy, tileKey, tilesToDraw, tx, ty;
+    var u_tileOffset = new Float32Array(4);
+    var i, ii, tileKey, tilesToDraw;
     for (i = 0, ii = zs.length; i < ii; ++i) {
       tilesToDraw = tilesToDrawByZ[zs[i]];
       for (tileKey in tilesToDraw) {
         tile = tilesToDraw[tileKey];
         tileExtent = tileGrid.getTileCoordExtent(tile.tileCoord, tmpExtent);
-        sx = 2 * (tileExtent[2] - tileExtent[0]) /
+        u_tileOffset[0] = 2 * (tileExtent[2] - tileExtent[0]) /
             framebufferExtentDimension;
-        sy = 2 * (tileExtent[3] - tileExtent[1]) /
+        u_tileOffset[1] = 2 * (tileExtent[3] - tileExtent[1]) /
             framebufferExtentDimension;
-        tx = 2 * (tileExtent[0] - framebufferExtent[0]) /
+        u_tileOffset[2] = 2 * (tileExtent[0] - framebufferExtent[0]) /
             framebufferExtentDimension - 1;
-        ty = 2 * (tileExtent[1] - framebufferExtent[1]) /
+        u_tileOffset[3] = 2 * (tileExtent[1] - framebufferExtent[1]) /
             framebufferExtentDimension - 1;
-        goog.vec.Vec4.setFromValues(u_tileOffset, sx, sy, tx, ty);
         gl.uniform4fv(this.locations_.u_tileOffset, u_tileOffset);
         mapRenderer.bindTileTexture(tile, tilePixelSize,
             tileGutter * pixelRatio, goog.webgl.LINEAR, goog.webgl.LINEAR);
@@ -354,26 +351,21 @@ ol.renderer.webgl.TileLayer.prototype.prepareFrame = function(frameState, layerS
   this.updateLogos(frameState, tileSource);
 
   var texCoordMatrix = this.texCoordMatrix;
-  goog.vec.Mat4.makeIdentity(texCoordMatrix);
-  goog.vec.Mat4.translate(texCoordMatrix,
+  ol.transform.reset(texCoordMatrix);
+  ol.transform.translate(texCoordMatrix,
       (center[0] - framebufferExtent[0]) /
           (framebufferExtent[2] - framebufferExtent[0]),
       (center[1] - framebufferExtent[1]) /
-          (framebufferExtent[3] - framebufferExtent[1]),
-      0);
+          (framebufferExtent[3] - framebufferExtent[1]));
   if (viewState.rotation !== 0) {
-    goog.vec.Mat4.rotateZ(texCoordMatrix, viewState.rotation);
+    ol.transform.rotate(texCoordMatrix, viewState.rotation);
   }
-  goog.vec.Mat4.scale(texCoordMatrix,
+  ol.transform.scale(texCoordMatrix,
       frameState.size[0] * viewState.resolution /
           (framebufferExtent[2] - framebufferExtent[0]),
       frameState.size[1] * viewState.resolution /
-          (framebufferExtent[3] - framebufferExtent[1]),
-      1);
-  goog.vec.Mat4.translate(texCoordMatrix,
-      -0.5,
-      -0.5,
-      0);
+          (framebufferExtent[3] - framebufferExtent[1]));
+  ol.transform.translate(texCoordMatrix, -0.5, -0.5);
 
   return true;
 };
@@ -391,9 +383,8 @@ ol.renderer.webgl.TileLayer.prototype.forEachLayerAtPixel = function(pixel, fram
     pixel[0] / frameState.size[0],
     (frameState.size[1] - pixel[1]) / frameState.size[1]];
 
-  var pixelOnFrameBufferScaled = [0, 0];
-  ol.vec.Mat4.multVec2(
-      this.texCoordMatrix, pixelOnMapScaled, pixelOnFrameBufferScaled);
+  var pixelOnFrameBufferScaled = ol.transform.apply(
+      this.texCoordMatrix, pixelOnMapScaled.slice());
   var pixelOnFrameBuffer = [
     pixelOnFrameBufferScaled[0] * this.framebufferDimension,
     pixelOnFrameBufferScaled[1] * this.framebufferDimension];
diff --git a/src/ol/renderer/webgl/webglvectorlayerrenderer.js b/src/ol/renderer/webgl/webglvectorlayerrenderer.js
index 482bfa11af..7e1c210975 100644
--- a/src/ol/renderer/webgl/webglvectorlayerrenderer.js
+++ b/src/ol/renderer/webgl/webglvectorlayerrenderer.js
@@ -5,10 +5,10 @@ goog.require('ol.events');
 goog.require('ol.ViewHint');
 goog.require('ol.extent');
 goog.require('ol.layer.Vector');
+goog.require('ol.transform');
 goog.require('ol.render.webgl.ReplayGroup');
 goog.require('ol.renderer.vector');
 goog.require('ol.renderer.webgl.Layer');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -154,9 +154,8 @@ ol.renderer.webgl.VectorLayer.prototype.hasFeatureAtCoordinate = function(coordi
  * @inheritDoc
  */
 ol.renderer.webgl.VectorLayer.prototype.forEachLayerAtPixel = function(pixel, frameState, callback, thisArg) {
-  var coordinate = pixel.slice();
-  ol.vec.Mat4.multVec2(
-      frameState.pixelToCoordinateMatrix, coordinate, coordinate);
+  var coordinate = ol.transform.apply(
+      frameState.pixelToCoordinateTransform, pixel.slice());
   var hasFeature = this.hasFeatureAtCoordinate(coordinate, frameState);
 
   if (hasFeature) {
diff --git a/src/ol/source/imagevectorsource.js b/src/ol/source/imagevectorsource.js
index c601e41eae..f7e9324523 100644
--- a/src/ol/source/imagevectorsource.js
+++ b/src/ol/source/imagevectorsource.js
@@ -3,7 +3,7 @@ goog.provide('ol.source.ImageVector');
 goog.require('goog.asserts');
 goog.require('ol.events');
 goog.require('ol.events.EventType');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.dom');
 goog.require('ol.extent');
 goog.require('ol.render.canvas.ReplayGroup');
@@ -11,7 +11,6 @@ goog.require('ol.renderer.vector');
 goog.require('ol.source.ImageCanvas');
 goog.require('ol.source.Vector');
 goog.require('ol.style.Style');
-goog.require('ol.vec.Mat4');
 
 
 /**
@@ -41,9 +40,9 @@ ol.source.ImageVector = function(options) {
 
   /**
    * @private
-   * @type {!goog.vec.Mat4.Number}
+   * @type {ol.Transform}
    */
-  this.transform_ = goog.vec.Mat4.createNumber();
+  this.transform_ = ol.transform.create();
 
   /**
    * @private
@@ -212,15 +211,18 @@ ol.source.ImageVector.prototype.getStyleFunction = function() {
  * @param {number} resolution Resolution.
  * @param {number} pixelRatio Pixel ratio.
  * @param {ol.Size} size Size.
- * @return {!goog.vec.Mat4.Number} Transform.
+ * @return {!ol.Transform} Transform.
  * @private
  */
 ol.source.ImageVector.prototype.getTransform_ = function(center, resolution, pixelRatio, size) {
-  return ol.vec.Mat4.makeTransform2D(this.transform_,
-      size[0] / 2, size[1] / 2,
-      pixelRatio / resolution, -pixelRatio / resolution,
-      0,
-      -center[0], -center[1]);
+  var dx1 = size[0] / 2;
+  var dy1 = size[1] / 2;
+  var sx = pixelRatio / resolution;
+  var sy = -sx;
+  var dx2 = -center[0];
+  var dy2 = -center[1];
+
+  return ol.transform.compose(this.transform_, dx1, dy1, sx, sy, 0, dx2, dy2);
 };
 
 
diff --git a/src/ol/source/rastersource.js b/src/ol/source/rastersource.js
index 2b1d6478ca..f6759297e2 100644
--- a/src/ol/source/rastersource.js
+++ b/src/ol/source/rastersource.js
@@ -4,7 +4,7 @@ goog.provide('ol.source.RasterEvent');
 goog.provide('ol.source.RasterEventType');
 
 goog.require('goog.asserts');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.ImageCanvas');
 goog.require('ol.TileQueue');
 goog.require('ol.dom');
@@ -120,7 +120,7 @@ ol.source.Raster = function(options) {
   this.frameState_ = {
     animate: false,
     attributions: {},
-    coordinateToPixelMatrix: goog.vec.Mat4.createNumber(),
+    coordinateToPixelTransform: ol.transform.create(),
     extent: null,
     focus: null,
     index: 0,
@@ -128,7 +128,7 @@ ol.source.Raster = function(options) {
     layerStatesArray: layerStatesArray,
     logos: {},
     pixelRatio: 1,
-    pixelToCoordinateMatrix: goog.vec.Mat4.createNumber(),
+    pixelToCoordinateTransform: ol.transform.create(),
     postRenderFunctions: [],
     size: [0, 0],
     skippedFeatureUids: {},
diff --git a/src/ol/transform.js b/src/ol/transform.js
new file mode 100644
index 0000000000..b028d13158
--- /dev/null
+++ b/src/ol/transform.js
@@ -0,0 +1,229 @@
+goog.provide('ol.transform');
+
+/**
+ * Collection of affine 2d transformation functions. The functions work on an
+ * array of 6 elements. The element order is compatible with the [SVGMatrix
+ * interface](https://developer.mozilla.org/en-US/docs/Web/API/SVGMatrix) and is
+ * a subset (elements a to f) of a 3x3 martrix:
+ * ```
+ * [ a c e ]
+ * [ b d f ]
+ * [ 0 0 1 ]
+ * ```
+ */
+
+
+/**
+ * @private
+ * @type {ol.Transform}
+ */
+ol.transform.tmp_ = new Array(6);
+
+
+/**
+ * Create an identity transform.
+ * @return {!ol.Transform} Identity transform.
+ */
+ol.transform.create = function() {
+  return [1, 0, 0, 1, 0, 0];
+};
+
+
+/**
+ * Resets the given transform to an identity transform.
+ * @param {!ol.Transform} transform Transform.
+ * @return {!ol.Transform} Transform.
+ */
+ol.transform.reset = function(transform) {
+  return ol.transform.set(transform, 1, 0, 0, 1, 0, 0);
+};
+
+
+/**
+ * Multiply the underlying matrices of two transforms and return the result in
+ * the first transform.
+ * @param {!ol.Transform} transform1 Transform parameters of matrix 1.
+ * @param {!ol.Transform} transform2 Transform parameters of matrix 2.
+ * @return {!ol.Transform} transform1 multiplied with transform2.
+ */
+ol.transform.multiply = function(transform1, transform2) {
+  var a1 = transform1[0];
+  var b1 = transform1[1];
+  var c1 = transform1[2];
+  var d1 = transform1[3];
+  var e1 = transform1[4];
+  var f1 = transform1[5];
+  var a2 = transform2[0];
+  var b2 = transform2[1];
+  var c2 = transform2[2];
+  var d2 = transform2[3];
+  var e2 = transform2[4];
+  var f2 = transform2[5];
+
+  transform1[0] = a1 * a2 + c1 * b2;
+  transform1[1] = b1 * a2 + d1 * b2;
+  transform1[2] = a1 * c2 + c1 * d2;
+  transform1[3] = b1 * c2 + d1 * d2;
+  transform1[4] = a1 * e2 + c1 * f2 + e1;
+  transform1[5] = b1 * e2 + d1 * f2 + f1;
+
+  return transform1;
+};
+
+/**
+ * Set the transform components a-f on a given transform.
+ * @param {!ol.Transform} transform Transform.
+ * @param {number} a The a component of the transform.
+ * @param {number} b The b component of the transform.
+ * @param {number} c The c component of the transform.
+ * @param {number} d The d component of the transform.
+ * @param {number} e The e component of the transform.
+ * @param {number} f The f component of the transform.
+ * @return {!ol.Transform} Matrix with transform applied.
+ */
+ol.transform.set = function(transform, a, b, c, d, e, f) {
+  transform[0] = a;
+  transform[1] = b;
+  transform[2] = c;
+  transform[3] = d;
+  transform[4] = e;
+  transform[5] = f;
+  return transform;
+};
+
+
+/**
+ * Set transform on one matrix from another matrix.
+ * @param {!ol.Transform} transform1 Matrix to set transform to.
+ * @param {!ol.Transform} transform2 Matrix to set transform from.
+ * @return {!ol.Transform} transform1 with transform from transform2 applied.
+ */
+ol.transform.setFromArray = function(transform1, transform2) {
+  transform1[0] = transform2[0];
+  transform1[1] = transform2[1];
+  transform1[2] = transform2[2];
+  transform1[3] = transform2[3];
+  transform1[4] = transform2[4];
+  transform1[5] = transform2[5];
+  return transform1;
+};
+
+
+/**
+ * Transforms the given coordinate with the given transform returning the
+ * resulting, transformed coordinate. The coordinate will be modified in-place.
+ *
+ * @param {ol.Transform} transform The transformation.
+ * @param {ol.Coordinate|ol.Pixel} coordinate The coordinate to transform.
+ * @return {ol.Coordinate|ol.Pixel} return coordinate so that operations can be
+ *     chained together.
+ */
+ol.transform.apply = function(transform, coordinate) {
+  var x = coordinate[0], y = coordinate[1];
+  coordinate[0] = transform[0] * x + transform[2] * y + transform[4];
+  coordinate[1] = transform[1] * x + transform[3] * y + transform[5];
+  return coordinate;
+};
+
+
+/**
+ * Applies rotation to the given transform.
+ * @param {!ol.Transform} transform Transform.
+ * @param {number} angle Angle in radians.
+ * @return {!ol.Transform} The rotated transform.
+ */
+ol.transform.rotate = function(transform, angle) {
+  var cos = Math.cos(angle);
+  var sin = Math.sin(angle);
+  return ol.transform.multiply(transform,
+      ol.transform.set(ol.transform.tmp_, cos, sin, -sin, cos, 0, 0));
+};
+
+
+/**
+ * Applies scale to a given transform.
+ * @param {!ol.Transform} transform Transform.
+ * @param {number} x Scale factor x.
+ * @param {number} y Scale factor y.
+ * @return {!ol.Transform} The scaled transform.
+ */
+ol.transform.scale = function(transform, x, y) {
+  return ol.transform.multiply(transform,
+      ol.transform.set(ol.transform.tmp_, x, 0, 0, y, 0, 0));
+};
+
+
+/**
+ * Applies translation to the given transform.
+ * @param {!ol.Transform} transform Transform.
+ * @param {number} dx Translation x.
+ * @param {number} dy Translation y.
+ * @return {!ol.Transform} The translated transform.
+ */
+ol.transform.translate = function(transform, dx, dy) {
+  return ol.transform.multiply(transform,
+      ol.transform.set(ol.transform.tmp_, 1, 0, 0, 1, dx, dy));
+};
+
+
+/**
+ * Creates a composite transform given an initial translation, scale, rotation, and
+ * final translation (in that order only, not commutative).
+ * @param {!ol.Transform} transform The transform (will be modified in place).
+ * @param {number} dx1 Initial translation x.
+ * @param {number} dy1 Initial translation y.
+ * @param {number} sx Scale factor x.
+ * @param {number} sy Scale factor y.
+ * @param {number} angle Rotation (in counter-clockwise radians).
+ * @param {number} dx2 Final translation x.
+ * @param {number} dy2 Final translation y.
+ * @return {!ol.Transform} The composite transform.
+ */
+ol.transform.compose = function(transform, dx1, dy1, sx, sy, angle, dx2, dy2) {
+  var sin = Math.sin(angle);
+  var cos = Math.cos(angle);
+  transform[0] = sx * cos;
+  transform[1] = sy * sin;
+  transform[2] = -sx * sin;
+  transform[3] = sy * cos;
+  transform[4] = dx2 * sx * cos - dy2 * sx * sin + dx1;
+  transform[5] = dx2 * sy * sin + dy2 * sy * cos + dy1;
+  return transform;
+};
+
+
+/**
+ * Invert the given transform.
+ * @param {!ol.Transform} transform Transform.
+ * @return {!ol.Transform} Inverse of the transform.
+ */
+ol.transform.invert = function(transform) {
+  var det = ol.transform.determinant(transform);
+  goog.asserts.assert(det !== 0, 'Transformation matrix cannot be inverted.');
+
+  var a = transform[0];
+  var b = transform[1];
+  var c = transform[2];
+  var d = transform[3];
+  var e = transform[4];
+  var f = transform[5];
+
+  transform[0] = d / det;
+  transform[1] = -b / det;
+  transform[2] = -c / det;
+  transform[3] = a / det;
+  transform[4] = (c * f - d * e) / det;
+  transform[5] = -(a * f - b * e) / det;
+
+  return transform;
+};
+
+
+/**
+ * Returns the determinant of the given matrix.
+ * @param {!ol.Transform} mat Matrix.
+ * @return {number} Determinant.
+ */
+ol.transform.determinant = function(mat) {
+  return mat[0] * mat[3] - mat[1] * mat[2];
+};
diff --git a/src/ol/typedefs.js b/src/ol/typedefs.js
index c9a59f1eab..506ae41225 100644
--- a/src/ol/typedefs.js
+++ b/src/ol/typedefs.js
@@ -329,6 +329,14 @@ ol.LRUCacheEntry;
 ol.MapOptionsInternal;
 
 
+/**
+ * An array representing an affine 2d transformation for use with
+ * {@link ol.transform} functions. The array has 6 elements.
+ * @typedef {Array.<number>}
+ */
+ol.Transform;
+
+
 /**
  * @typedef {{depth: (Array.<number>|undefined),
  *            feature: ol.Feature,
diff --git a/src/ol/vec/mat4.js b/src/ol/vec/mat4.js
index 4fa6f5ca77..65dd22f1e4 100644
--- a/src/ol/vec/mat4.js
+++ b/src/ol/vec/mat4.js
@@ -1,90 +1,25 @@
 goog.provide('ol.vec.Mat4');
-goog.provide('ol.vec.Mat4.Number');
-
-goog.require('goog.vec.Mat4');
 
 
 /**
- * A alias for the goog.vec.Number type.
- * @typedef {goog.vec.Number}
+ * @return {Array.<number>} 4x4 matrix representing a 3D identity transform.
  */
-ol.vec.Mat4.Number;
-
-
-/**
- * @param {!goog.vec.Mat4.Number} mat Matrix.
- * @param {number} translateX1 Translate X1.
- * @param {number} translateY1 Translate Y1.
- * @param {number} scaleX Scale X.
- * @param {number} scaleY Scale Y.
- * @param {number} rotation Rotation.
- * @param {number} translateX2 Translate X2.
- * @param {number} translateY2 Translate Y2.
- * @return {!goog.vec.Mat4.Number} Matrix.
- */
-ol.vec.Mat4.makeTransform2D = function(mat, translateX1, translateY1,
-    scaleX, scaleY, rotation, translateX2, translateY2) {
-  goog.vec.Mat4.makeIdentity(mat);
-  if (translateX1 !== 0 || translateY1 !== 0) {
-    goog.vec.Mat4.translate(mat, translateX1, translateY1, 0);
-  }
-  if (scaleX != 1 || scaleY != 1) {
-    goog.vec.Mat4.scale(mat, scaleX, scaleY, 1);
-  }
-  if (rotation !== 0) {
-    goog.vec.Mat4.rotateZ(mat, rotation);
-  }
-  if (translateX2 !== 0 || translateY2 !== 0) {
-    goog.vec.Mat4.translate(mat, translateX2, translateY2, 0);
-  }
-  return mat;
+ol.vec.Mat4.create = function() {
+  return [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1];
 };
 
 
 /**
- * Returns true if mat1 and mat2 represent the same 2D transformation.
- * @param {goog.vec.Mat4.Number} mat1 Matrix 1.
- * @param {goog.vec.Mat4.Number} mat2 Matrix 2.
- * @return {boolean} Equal 2D.
+ * @param {Array.<number>} mat4 Flattened 4x4 matrix receiving the result.
+ * @param {ol.Transform} transform Transformation matrix.
+ * @return {Array.<number>} 2D transformation matrix as flattened 4x4 matrix.
  */
-ol.vec.Mat4.equals2D = function(mat1, mat2) {
-  return (
-      goog.vec.Mat4.getElement(mat1, 0, 0) ==
-      goog.vec.Mat4.getElement(mat2, 0, 0) &&
-      goog.vec.Mat4.getElement(mat1, 1, 0) ==
-      goog.vec.Mat4.getElement(mat2, 1, 0) &&
-      goog.vec.Mat4.getElement(mat1, 0, 1) ==
-      goog.vec.Mat4.getElement(mat2, 0, 1) &&
-      goog.vec.Mat4.getElement(mat1, 1, 1) ==
-      goog.vec.Mat4.getElement(mat2, 1, 1) &&
-      goog.vec.Mat4.getElement(mat1, 0, 3) ==
-      goog.vec.Mat4.getElement(mat2, 0, 3) &&
-      goog.vec.Mat4.getElement(mat1, 1, 3) ==
-      goog.vec.Mat4.getElement(mat2, 1, 3));
-};
-
-
-/**
- * Transforms the given vector with the given matrix storing the resulting,
- * transformed vector into resultVec. The input vector is multiplied against the
- * upper 2x4 matrix omitting the projective component.
- *
- * @param {goog.vec.Mat4.Number} mat The matrix supplying the transformation.
- * @param {Array.<number>} vec The 3 element vector to transform.
- * @param {Array.<number>} resultVec The 3 element vector to receive the results
- *     (may be vec).
- * @return {Array.<number>} return resultVec so that operations can be
- *     chained together.
- */
-ol.vec.Mat4.multVec2 = function(mat, vec, resultVec) {
-  var m00 = goog.vec.Mat4.getElement(mat, 0, 0);
-  var m10 = goog.vec.Mat4.getElement(mat, 1, 0);
-  var m01 = goog.vec.Mat4.getElement(mat, 0, 1);
-  var m11 = goog.vec.Mat4.getElement(mat, 1, 1);
-  var m03 = goog.vec.Mat4.getElement(mat, 0, 3);
-  var m13 = goog.vec.Mat4.getElement(mat, 1, 3);
-  var x = vec[0], y = vec[1];
-  resultVec[0] = m00 * x + m01 * y + m03;
-  resultVec[1] = m10 * x + m11 * y + m13;
-  return resultVec;
+ol.vec.Mat4.fromTransform = function(mat4, transform) {
+  mat4[0] = transform[0];
+  mat4[1] = transform[1];
+  mat4[4] = transform[2];
+  mat4[5] = transform[3];
+  mat4[12] = transform[4];
+  mat4[13] = transform[5];
+  return mat4;
 };
diff --git a/test/spec/ol/dom/dom.test.js b/test/spec/ol/dom/dom.test.js
index d53e4552f9..9a20b5ad7d 100644
--- a/test/spec/ol/dom/dom.test.js
+++ b/test/spec/ol/dom/dom.test.js
@@ -147,8 +147,8 @@ describe('ol.dom', function() {
 
   describe('ol.dom.transformElement2D', function() {
     var element = null;
-    var transform = goog.vec.Mat4.createNumber();
-    var transformFloat = goog.vec.Mat4.createNumber();
+    var transform = ol.transform.create();
+    var transformFloat = ol.transform.create();
     transformFloat[0] = 0.12345;
     beforeEach(function() {
       element = document.createElement('div');
@@ -564,5 +564,5 @@ describe('ol.dom', function() {
 });
 
 goog.require('goog.userAgent');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.dom');
diff --git a/test/spec/ol/extent.test.js b/test/spec/ol/extent.test.js
index dfeb399716..ea9f000a5f 100644
--- a/test/spec/ol/extent.test.js
+++ b/test/spec/ol/extent.test.js
@@ -864,7 +864,6 @@ describe('ol.extent', function() {
 });
 
 
-goog.require('goog.vec.Mat4');
 goog.require('ol.extent');
 goog.require('ol.extent.Corner');
 goog.require('ol.extent.Relationship');
diff --git a/test/spec/ol/geom/flat/transformflatgeom.test.js b/test/spec/ol/geom/flat/transformflatgeom.test.js
index 6bb9b564c9..c268af60e5 100644
--- a/test/spec/ol/geom/flat/transformflatgeom.test.js
+++ b/test/spec/ol/geom/flat/transformflatgeom.test.js
@@ -23,9 +23,11 @@ describe('ol.geom.flat.transform', function() {
           [-82.128838, 26.693342, 0],
           [-82.102127, 26.585724, 0]]]
       ]).transform('EPSG:4326', 'EPSG:3857');
-      var transform = [0.0004088332670837288, 0, 0, 0, 0,
-        -0.0004088332670837288, 0, 0, 0, 0, 1, 0, 4480.991370439071,
-        1529.5752568707105, 0, 1];
+      var transform = [
+        0.0004088332670837288, 0,
+        0, -0.0004088332670837288,
+        4480.991370439071, 1529.5752568707105
+      ];
       var pixelCoordinates = ol.geom.transformSimpleGeometry2D(
           multiPolygonGeometry, transform, []);
       expect(pixelCoordinates[0]).to.roughlyEqual(806.6035275946265, 1e-9);
diff --git a/test/spec/ol/render.test.js b/test/spec/ol/render.test.js
index 662ad0fb4c..890c8aa0f1 100644
--- a/test/spec/ol/render.test.js
+++ b/test/spec/ol/render.test.js
@@ -22,16 +22,16 @@ describe('ol.render', function() {
           [0, 0, size[0] * pixelRatio, size[1] * pixelRatio]);
       expect(canvas.style.width).to.be(size[0] + 'px');
       expect(canvas.style.height).to.be(size[1] + 'px');
-      var transform = ol.vec.Mat4.makeTransform2D(goog.vec.Mat4.createNumber(),
-          0, 0, pixelRatio, pixelRatio, 0, 0, 0);
-      expect(ol.vec.Mat4.equals2D(render.transform_, transform)).to.be.ok();
+      var transform = ol.transform.scale(ol.transform.create(),
+          pixelRatio, pixelRatio);
+      expect(ol.array.equals(render.transform_, transform)).to.be.ok();
     });
   });
 
 });
 
 
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.render');
 goog.require('ol.render.canvas.Immediate');
 goog.require('ol.vec.Mat4');
diff --git a/test/spec/ol/render/canvasimmediate.test.js b/test/spec/ol/render/canvasimmediate.test.js
index 132fc0e4dc..c182fe5ed8 100644
--- a/test/spec/ol/render/canvasimmediate.test.js
+++ b/test/spec/ol/render/canvasimmediate.test.js
@@ -198,10 +198,9 @@ describe('ol.render.canvas.Immediate', function() {
       };
 
       var transform = [
-        0.0004088332670837288, 0, 0, 0,
-        0, -0.0004088332670837288, 0, 0,
-        0, 0, 1, 0,
-        4480.991370439071, 1529.5752568707105, 0, 1
+        0.0004088332670837288, 0,
+        0, -0.0004088332670837288,
+        4480.991370439071, 1529.5752568707105
       ];
 
       var extent = [
diff --git a/test/spec/ol/renderer/canvas/canvaslayerrenderer.test.js b/test/spec/ol/renderer/canvas/canvaslayerrenderer.test.js
index 2dead6d8c0..eb132a58cb 100644
--- a/test/spec/ol/renderer/canvas/canvaslayerrenderer.test.js
+++ b/test/spec/ol/renderer/canvas/canvaslayerrenderer.test.js
@@ -23,11 +23,11 @@ describe('ol.renderer.canvas.Layer', function() {
         },
         size: [10, 10],
         pixelRatio: 1,
-        coordinateToPixelMatrix: goog.vec.Mat4.createNumber(),
-        pixelToCoordinateMatrix: goog.vec.Mat4.createNumber()
+        coordinateToPixelTransform: ol.transform.create(),
+        pixelToCoordinateTransform: ol.transform.create()
       };
       renderer.getImageTransform = function() {
-        return goog.vec.Mat4.createNumberIdentity();
+        return ol.transform.create();
       };
       ol.renderer.Map.prototype.calculateMatrices2D(frameState);
       var layerState = layer.getLayerState();
@@ -62,7 +62,7 @@ describe('ol.renderer.canvas.Layer', function() {
 
 
 goog.require('ol.render.canvas');
-goog.require('goog.vec.Mat4');
+goog.require('ol.transform');
 goog.require('ol.layer.Image');
 goog.require('ol.renderer.Map');
 goog.require('ol.renderer.canvas.Layer');
diff --git a/test/spec/ol/renderer/webgl/webglimagelayerrenderer.test.js b/test/spec/ol/renderer/webgl/webglimagelayerrenderer.test.js
index 663cff60f3..b87b571838 100644
--- a/test/spec/ol/renderer/webgl/webglimagelayerrenderer.test.js
+++ b/test/spec/ol/renderer/webgl/webglimagelayerrenderer.test.js
@@ -49,39 +49,30 @@ describe('ol.renderer.webgl.ImageLayer', function() {
           pixelRatio, viewCenter, viewResolution, viewRotation, imageExtent);
       var matrix = renderer.getProjectionMatrix();
 
-      var input;
-      var output = goog.vec.Vec4.createNumber();
-
-      input = goog.vec.Vec4.createFromValues(-1, -1, 0, 1);
-      goog.vec.Mat4.multVec4(matrix, input, output);
+      var output = ol.transform.apply(matrix, [-1, -1]);
       expect(output[0]).to.eql(-6);
       expect(output[1]).to.eql(-6);
 
-      input = goog.vec.Vec4.createFromValues(1, -1, 0, 1);
-      goog.vec.Mat4.multVec4(matrix, input, output);
+      output = ol.transform.apply(matrix, [1, -1]);
       expect(output[0]).to.eql(2);
       expect(output[1]).to.eql(-6);
 
-      input = goog.vec.Vec4.createFromValues(-1, 1, 0, 1);
-      goog.vec.Mat4.multVec4(matrix, input, output);
+      output = ol.transform.apply(matrix, [-1, 1]);
       expect(output[0]).to.eql(-6);
       expect(output[1]).to.eql(6);
 
-      input = goog.vec.Vec4.createFromValues(1, 1, 0, 1);
-      goog.vec.Mat4.multVec4(matrix, input, output);
+      output = ol.transform.apply(matrix, [1, 1]);
       expect(output[0]).to.eql(2);
       expect(output[1]).to.eql(6);
 
-      input = goog.vec.Vec4.createFromValues(0, 0, 0, 1);
-      goog.vec.Mat4.multVec4(matrix, input, output);
+      output = ol.transform.apply(matrix, [0, 0]);
       expect(output[0]).to.eql(-2);
       expect(output[1]).to.eql(0);
     });
   });
 });
 
-goog.require('goog.vec.Mat4');
-goog.require('goog.vec.Vec4');
+goog.require('ol.transform');
 goog.require('ol.Map');
 goog.require('ol.proj.common');
 goog.require('ol.layer.Image');
diff --git a/test/spec/ol/transform.test.js b/test/spec/ol/transform.test.js
new file mode 100644
index 0000000000..b838a91ae9
--- /dev/null
+++ b/test/spec/ol/transform.test.js
@@ -0,0 +1,121 @@
+goog.provide('ol.test.transform');
+
+describe('ol.transform', function() {
+
+  function assertRoughlyEqual(t1, t2) {
+    t1.forEach(function(item, index) {
+      expect(item).to.roughlyEqual(t2[index], 1e-8);
+    });
+  }
+
+  describe('ol.transform.create()', function() {
+    it('creates an identity transform', function() {
+      expect(ol.transform.create()).to.eql([1, 0, 0, 1, 0, 0]);
+    });
+  });
+
+  describe('ol.transform.reset()', function() {
+    it('resets tansform to an identity transform', function() {
+      var transform = [1, 2, 3, 4, 5, 6];
+      expect(ol.transform.reset(transform)).to.eql([1, 0, 0, 1, 0, 0]);
+      expect(transform).to.eql([1, 0, 0, 1, 0, 0]);
+    });
+  });
+
+  describe('ol.transform.set()', function() {
+    it('sets the given values', function() {
+      var transform = ol.transform.create();
+      expect(ol.transform.set(transform, 1, 2, 3, 4, 5, 6)).to.eql([1, 2, 3, 4, 5, 6]);
+      expect(transform).to.eql([1, 2, 3, 4, 5, 6]);
+    });
+  });
+
+  describe('ol.transform.setFromArray()', function() {
+    it('sets values of 2nd transform on 1st transform', function() {
+      var transform1 = ol.transform.create();
+      var transform2 = [1, 2, 3, 4, 5, 6];
+      expect(ol.transform.setFromArray(transform1, transform2)).to.eql(transform2);
+      expect(transform1).to.eql(transform2);
+    });
+  });
+
+  describe('ol.transform.translate()', function() {
+    it('applies translation to a transform', function() {
+      var transform = ol.transform.create();
+      expect(ol.transform.translate(transform, 3, 4)).to.eql([1, 0, 0, 1, 3, 4]);
+      expect(transform).to.eql([1, 0, 0, 1, 3, 4]);
+    });
+  });
+
+  describe('ol.transform.scale()', function() {
+    it('applies scaling to a transform', function() {
+      var transform = ol.transform.create();
+      expect(ol.transform.scale(transform, 3, 4)).to.eql([3, 0, 0, 4, 0, 0]);
+      expect(transform).to.eql([3, 0, 0, 4, 0, 0]);
+    });
+  });
+
+  describe('ol.transform.rotate()', function() {
+    it('applies rotation to a transform', function() {
+      var transform = ol.transform.create();
+      assertRoughlyEqual(ol.transform.rotate(transform, Math.PI / 2), [0, 1, -1, 0, 0, 0]);
+      assertRoughlyEqual(transform, [0, 1, -1, 0, 0, 0]);
+    });
+  });
+
+  describe('ol.transform.multiply()', function() {
+    it('multiplies two transforms', function() {
+      var transform1 = [1, 2, 1, 2, 1, 2];
+      var transform2 = [1, 2, 1, 2, 1, 2];
+      expect(ol.transform.multiply(transform1, transform2)).to.eql([3, 6, 3, 6, 4, 8]);
+      expect(transform1).to.eql([3, 6, 3, 6, 4, 8]);
+    });
+  });
+
+  describe('ol.transform.compose()', function() {
+    it('composes a translate, scale, rotate, translate transform', function() {
+      var dx1 = 3;
+      var dy1 = 4;
+      var sx = 1.5;
+      var sy = -1.5;
+      var angle = Math.PI / 3;
+      var dx2 = -dx1 / 2;
+      var dy2 = -dy1 / 2;
+
+      var expected = ol.transform.create();
+      ol.transform.translate(expected, dx1, dy1);
+      ol.transform.scale(expected, sx, sy);
+      ol.transform.rotate(expected, angle);
+      ol.transform.translate(expected, dx2, dy2);
+
+      var composed = ol.transform.create();
+      var composedReturn = ol.transform.compose(composed, dx1, dy1, sx, sy, angle, dx2, dy2);
+      expect(composed).to.equal(composedReturn);
+      expect(composed).to.eql(expected);
+    });
+  });
+
+  describe('ol.transform.invert()', function() {
+    it('inverts a transform', function() {
+      var transform = [1, 0, 1, 0, 1, 0];
+      expect(function() {
+        ol.transform.invert(transform);
+      }).to.throwException();
+      transform = [1, 1, 1, 2, 2, 0];
+      expect(ol.transform.invert(transform)).to.eql([2, -1, -1, 1, -4, 2]);
+      expect(transform).to.eql([2, -1, -1, 1, -4, 2]);
+    });
+  });
+
+  describe('ol.transform.apply()', function() {
+    it('applies a transform to a 2d vector', function() {
+      var transform = ol.transform.translate(ol.transform.create(), 2, 3);
+      var point = [1, 2];
+      expect(ol.transform.apply(transform, point)).to.eql([3, 5]);
+      expect(point).to.eql([3, 5]);
+    });
+  });
+
+});
+
+goog.require('ol.transform');
diff --git a/test/spec/ol/vec/mat4.test.js b/test/spec/ol/vec/mat4.test.js
new file mode 100644
index 0000000000..f034926e3d
--- /dev/null
+++ b/test/spec/ol/vec/mat4.test.js
@@ -0,0 +1,25 @@
+goog.provide('ol.test.vec.Mat4');
+
+describe('ol.vec.Mat4', function() {
+
+  describe('ol.vec.Mat4.create()', function() {
+    it('returns the expected matrix', function() {
+      expect(ol.vec.Mat4.create()).to.eql(
+            [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]);
+    });
+  });
+
+  describe('ol.vec.Mat4.fromTransform()', function() {
+    it('sets the expected transform on the matrix', function() {
+      var transform = [1, 2, 3, 4, 5, 6];
+      var result = ol.vec.Mat4.create();
+      expect(ol.vec.Mat4.fromTransform(result, transform)).to.eql(
+          [1, 2, 0, 0, 3, 4, 0, 0, 0, 0, 1, 0, 5, 6, 0, 1]);
+      expect(result).to.eql(
+          [1, 2, 0, 0, 3, 4, 0, 0, 0, 0, 1, 0, 5, 6, 0, 1]);
+    });
+  });
+
+});
+
+goog.require('ol.vec.Mat4');